Author's Notes: I'm now trying my hands at a crossover between my favourite TV show and a movie I unexpectedly liked very much.
The title is a quote from the Doctor Who episode The beast below, which inspired me to write this story. It is actually the first idea I had for a fic after watching Frozen.
Hope you'll have a good read!

"Elsa, do you want to build a snowman?"

Elsa cringed on her bed, feeling the temperature drop around her, desperately trying not to hear her sister. She had thought about singing to herself, but was afraid Anna might hear her and take this as an answer.

"Come on, it snowed a lot last night, the courtyard is completely white! We could build a snowman like before!"

Elsa rolled over, considering jamming her fingers into her ears. She knew it never worked anyway, and she would have to remove her gloves for that, which was frightening enough.

"Please, Elsa! I never manage to get Olaf right without you! When was the last time we did it together?"

Elsa finally snapped. She turned toward the door.

"Go away, Anna! I told you I don't want to play! Not today, not ever! I mean it!"

The princess managed to reach the end of her sentence before choking. It was always a mistake to answer. She hated the sound of her own voice when she was shouting at Anna. It was so hard not to let the pain show. More than everything, she hated hearing Anna answering her. She sounded so sad every time…

Elsa braced herself for the answer. That sad little "OK", or "Fine" that Anna let out before leaving. This time however there was only silence. Elsa strained her ear, wondering if she had not gone too far this time, and if she had not just heard a little sob muffled through the door.

Still nothing. Was it a new trick from Anna? She had been trying new plots to entice her sister out of her room recently, but nothing that could not be seen coming from a mile away. Silence was new, though.

Doing her best to move silently, the little princess let herself glide from her bed and inched toward the door, trying to listen for a breathing through the wood. She bit her lip to stop herself from calling her sister. She had to remember what her father was teaching her, concealing, not feeling. But right now she could not help feeling the guilt at the way she had spoken to her little sister.

She does not understand. I just want to protect her.

Elsa was now almost against the door, watching the little flowers of frost slowly form on its surface. The gloves protected the things she touched, but they could not do anything when she dropped the temperature of the room. She resisted the urge to peek through the keyhole. She knew Anna loved to do this and she dreaded seeing the eye of her sister waiting for her.

The princess jumped as an unearthly sound suddenly filled the silence. This was not her sister's voice, and she was not sure whether this could be her sister's doing. It sounded like a distant, groaning, wheezing complaint, rising and falling, and getting deeper and louder each time.

Elsa backed away. The sound kept growing, until it stopped with an almost musical chord. Then there was silence again. Elsa put her ear on the door, straining to hear. She thought she heard hinges creaking and people talking, but she could not make out the words clearly. The voices were unknown to her.

The young princess drew a deep breath. She really wanted to know where this noise had come from, but she did not want to fall prey to one of Anna's traps. Then again, she was still concerned about her sister, who she had sent away more brusquely that she had wanted. Maybe she could sneak an eye out, and learn the source of this noise, and at the same time check on Anna or warn her parents to do it.

Curiosity got the better of her. Trying her best to be silent, Elsa turned the door handle, which let out what seemed like a horrible grinding sound in the surrounding silence as the frost-coated latch gave way. Thankfully, the corridor behind the door was indeed empty.

Looking left and right, Elsa allowed herself a few steps outside of her room. Anna was nowhere to be seen or heard. What could be seen however, was a big blue wardrobe standing in the corridor a dozen meters away.

Elsa could not stop herself from moving closer to the incongruous object. She was sure it had not been there yesterday, and besides, it really made no sense to have a wardrobe there.

If it was a wardrobe. The thing had windows, for one thing. There were too high for her, though. Elsa gingerly walked around the strange cabinet. There was something written above the windows, but it made no sense to her. Police public call box?

"Hi!"

Elsa jumped against the wall. She felt the temperature around her drop again.

A woman was leaning against the strange box, smiling. She was dark-haired with a round face, and wore a rather short dress with black tights. Elsa vaguely wondered if she had not seen her before. But if she was a stranger…

"Sorry, I did not mean to startle you."

"Don't come closer!" Elsa shouted at the woman, who was looking as though she wanted to walk to her.

"Hey, don't be afraid, I won't hurt you." The woman crouched, bringing herself to eye level with Elsa while remaining on her side of the corridor.

"I'm Clara. What is your name?"

"I'm..." Elsa remembered her father's lessons. "I'm Princess Elsa of Arendelle. What are you doing in the castle?"

The woman's eyes twinkled.

"A princess? I'm honoured to meet you, your Highness."

Elsa could not decide whether the woman was serious or not, but her smile was definitely friendly.

"Did you come to see my… the King?"

"The King? I… don't think so. Should I see him?"

Elsa frowned. She was pretty sure strangers were not supposed to wander in the castle without seeming to be aware of her father. Actually they were not supposed to wander in the castle at all.

"How did you come here? The castle is closed."

"Oh, I came here with… a friend. He has a way with closed doors."

The woman stood up and made a tentative step toward Elsa.

"What is wrong? Are you afraid of something?"

"Don't come closer, please! I don't want to hurt you", Elsa shouted, flattening herself against the wall.

The woman cocked her head quizzically.

"Hurt me? How would you… OK, I'm staying right here. Look, I'm not moving any more. There is no risk of you hurting me if I remain here, right?"

Elsa relaxed a little.

"No I don't… I don't think so."

She glanced at the door of her room, still ajar. She could dash to it and lock the door behind her. This would mean the strange woman would still be at large in the castle, but whoever she was she did not deserve being struck by a stray shot of ice. Nobody did.

"Are you all right? Is something bothering you?"

The woman was looking at her with concern. Elsa began slowly inching toward her door.

"Listen… Elsa, if something or someone is threatening you, I'm sure my friend can help. He's very good for helping people with… special problems. Even problems no one would believe you had."

Elsa looked up. She knew she should be running to the safety of her room, or at the very least try to know if Anna was all right but… if this woman could really help…

"Does your friend know magic?"

The woman frowned, playing with one of her locks.

"You know", she said eventually, smiling, "I would not be surprised if he did." She leaned forward conspiratorially. "Of course he would use some fancy words instead, but it would still be magic."

Elsa hesitated. Her father had told her many times that the trolls in the mountain were the only ones who could help her with her magic, as the knowledge about it had been lost by man a long time ago, and even the trolls could not help her to control it. Even if this strange woman and her mysterious friend had some competence in magic, would they know about her own magic?

"Do you know about magic too?"

"Me? No. Well, I know some party tricks, but I never get them right anyway. And computers. I was really good with computers for a while, but that did not last. That's a kind of magic, I guess. But I don't think your problem is about computers."

Elsa found herself interested despite herself.

"Do you mean… sliding rules? That is not magic… I know how to use them", she added, unable to hide the pride in her voice. "I like mathematics."

The woman made a face.

"Good for you. I never liked that too much. Too strict and formal."

"I like how everything is so orderly with mathematics. They always give the same results from the same problems", Elsa could not stop herself from countering.

"That's one way to look at it, I guess." The woman smiled. "You know, maybe that's why I found all my maths teachers so dull. I've yet to meet one who is not boring me to tears."

"Oh, yes, teachers…" Elsa looked down sadly, reminded of the fact that her own maths teachers were mainly books and her parents, when they had time to teach her something other than etiquette, the duties of a queen, and the political situation of Arendelle.

"Geometry I liked, though", said the woman. Elsa looked up. "I knew how to make killer drawings with only a ruler and a compass."

"Oh, geometry is my favourite! It's everywhere you look! In the buildings, the mountains, the sky…"

"The frost, too", said the woman, showing the wall behind Elsa.

Elsa turned her head to look at the wall against which she had been flattening herself. A thin layer of frost had been slowly covering it, expanding from her.

"It's beautiful…" Elsa started at hearing the voice of the woman suddenly much closer. She had crossed the distance separating them and was concentrating on the frost on the wall. Elsa backed away.

"Please, don't come near me, I will hurt you…"

"You know, I think I remember there is some maths theory about the frost flowers", said the woman, dreamily, still concentrating on the wall. "Something about them being an example of naturally occurring fractals."

"Frac-tals?" asked Elsa, despite herself, still inching slowly away from the woman.

"Yeah. It's some mathematical thing that looks the same when you magnify it. Like snowflakes. Makes some pretty figures to put on T-shirts."

"Oh, so that's why snow is so easy to do" said Elsa almost without thinking. "You only have to show it how to start and it goes on by itself."

The woman turned her head to look at her quizzically.

"That's one way to look at it, I guess. I've never tried to make snow like that before." She smiled. "Did you?"

Elsa backed away.

"Look, I have to go, I should not be there. I'm sorry for the frost!"

"Why should you be sorry? You are not the one doing it, are you?" she asked jokingly. "Besides, I like it."

"Really?"

"Yeah. Yeah, I like the frost in winter. We are in winter, right?"

Elsa looked at the woman, puzzled. Was she making fun of her or was she really that clueless? You could not ignore the current season, especially with the temperature in the corridor being for once appropriate for winter.

"When I was a little girl around your age I loved to watch frost on the windows and imagine shapes in them. Don't you do that?"

"No", said Elsa hesitantly.

That was not entirely true. She had done that a few times, but it was mostly Anna who liked to discover new shapes in the frost that Elsa created on the windows. They had spend many hours like this, with Elsa creating little patterns of ice and Anna excitedly imagining stories with the shapes she saw in them. In the last two years the only things Elsa had seen in frost had been a ghastly reminder of the danger she was for the people she loved.

"Look, that one looks like a tree. And here, this looks like a leaf", the woman added, in a sadder voice. She turned her head to look at Elsa. "That's strange", she said, "why is there only frost here and where you are… Are you actually doing this?"

Elsa backed away, blubbering apologies. She felt the panic rise again in her. Conceal, don't feel.

"Wait!" called the woman. "This is beautiful. Are you really doing it? How are you doing that?"

Elsa hesitated. The situation was so unsettling it was hard to remember that she was supposed to lock herself in her room and try controlling her powers. Then again, she was somehow grateful to talk with somebody who was completely unknown for a change.

"I… can. Always could. But I can't control it."

The woman leaned against the defrosting wall.

"Why do you want to control it?" she asked softly.

"I could hurt people with it."

"But you are not hurting anyone with it. Actually I think you are doing beautiful things instead."

"I don't do it on purpose! And it's so easy to hurt people with it!"

The woman slowly sat on the ground, her back against the wall.

"Did you already hurt someone?" Elsa did not answer. The woman spoke softly after a few seconds. "It was an accident, right? Someone close?"

Elsa remained silent, nodding imperceptibly.

"Listen, Elsa", said the woman softly. "Accidents happen. You can hurt people even when it's the last thing you want to do. It can happen when you are trying to do something completely innocent. It can happen when you are trying to do something nice for them. It does not mean you have to stop doing it."

But I almost killed my sister. Do you have a sister?

"Do you understand? What you can do is amazing." The woman smiled. "But I can still ask my friend if he can help you to control it better."

"No, thank you. I think I will go back to my room, now."

"Wait!" called the woman, standing up. She leaned slowly toward Elsa. "Could you make some more frost flowers for me, please? I won't stand too close to you if it helps."

The woman's smile was contagious. Elsa could not stop a half smile to form on her lips as she pressed herself against the wall, watching the frost draw its little pathways as it expanded away from her.

Anna was slowly advancing in the gallery, glancing sadly at the paintings full of happy people surrounding her. She was trying very hard not to cry but could not stop the occasional sniffle.

"It's not fair!" she said eventually to no one in particular. "The snow was perfect for playing today, like we did before! It would only have been one snowman!"

She stifled a sob, then turned back to look at the painting of the woman on the swing near the door.

"I mean, I know she has to study to be a queen for when she is a grown up, but she does not have to study all the time! She can play some times too!"

Anna looked down, feeling a tear glide on her cheek.

"Why did she have to be so mean? I only wanted her to have fun playing with me…"

The door burst open.

"Hello! Hello! Coming through, don't mind me at all, just passing through!"

A tall man barged confidently in the room, then stopped and turned over himself a few times, taking in the paintings on the wall.

"Ohoh, a gallery! I love galleries! Hey", he said, striding purposefully toward the painting of the woman on the swing, "there is someone missing on this Fragonard! Cheeky woman that model", he added conspiratorially to Anna. "I think she had a thing for me actually. Do you know where I could meet the daughters of the King of Arendelle?"

Anna looked the man over, bewildered. He had ruffled hair, and wore a long waistcoat with a shirt and a bow tie. He was also completely unknown to her, which was something of a novelty in the last two years.

"Did you understand me?" he asked again, not unkindly. "I have a personal message to convey to the daughters of the King of Arendelle. And of the Queen, of course. That makes them the Princesses of Arendelle. Do you know where they are?"

"I am", said Anna, delighted at the distraction. "I am Princess Anna of Arendelle", she added, trying to curtsy and almost tripping herself in the process. "I have a sister, but she won't talk to me."

"Oh no", said the man exasperatedly, "you are even younger than before! I got the time wrong again! What is it with me and the time when I come here? What", he added, turning over himself, then pointing a finger at Anna, then at the various paintings on the wall, "is wrong! With me! And the time! Here!" he asked with emphasis.

"I don't know!" said Anna, backing away. "I'm sorry!"

"Sorry? Sorry for what? What should you feel sorry for?" asked the man, almost threateningly, advancing toward her. "So your sister has already begun not talking to you?" he asked, with a suddenly compassionate tone.

"Yes, for almost two years! She only says mean things now!" stuttered Anna. "I only asked her to build a snowman and she said she did not want to."

"She's wrong", said the man, crouching to be on her level. "You should always take the time to build snowmen with your sister. Unless of course they are animated by an alien entity bent on covering the world with snow, of course. Or if you are in a forest about to be destroyed by acid rain. Are you in a forest about to be destroyed by acid rain?"

"No! I'm in a castle! And there's plenty of snow in the courtyard. Fresh snow! It's the best for building snowmen!"

The man looked at her. Anna had not been able to keep the tremor out of her voice, and she felt another tear stinging her eye.

"And your sister made snowmen with you before?"

"Yes! Before she shut herself in her room we were always playing together but now she never comes out. My parents say it's because she has to learn to be a queen."

"Stop concealing" muttered the man, as if speaking for himself. He sighed. "You see, Anna, I'm supposed to do something about this but if I do it now I won't be asked to do it later and I can't let that happen. Or not happen." He looked at her with his penetrating, kind gaze for a few seconds, then appeared to reach a decision. "Tell you what, I will help you to build a snowman. It would be sad to let all this good snow unused, don't you think?"

"Yes!" shouted Anna. "We are going to build a snowman!" She paused. "Do you think my sister would come and see it when we are done?"

"Maybe", said the man, smiling non-committally. "OK, then, you lead the way. Let's build a snowman!"

The man strode resolutely toward a door. Anna ran after him and tugged on his coat.

"Err… the courtyard is this way…"

"Right! The courtyard! Let's go to the courtyard! I'm the Doctor by the way!"

Anna danced around the man as they walked in the empty corridors. She vaguely wondered what he was doing here, but she was too happy to have found someone with whom to build a snowman. Her parents seldom had time for this, and besides, it painfully reminded her of the few times all four of them had been playing in the snow.

They finally reached the big courtyard, white and silent. Anna shouted and jumped into the powder, then rolled around a bit before erupting again in front of the tall man.

"Can we build a snowman now, Sir Doctor?"

But the man had stopped and was looking around him with a perplexed expression.

"That courtyard..." he muttered.

The stranger walked a few steps into the snow before turning over himself, taking in the courtyard and the buildings surrounding it.

"Of course", he exclaimed suddenly, smacking his forehead. "Arendelle! I knew that name was ringing a bell!" He crouched and seized Anna's hand. "And your sister is named Elsa, right?"

Anna nodded, slightly perplexed by the man's behaviour, and vaguely afraid that he would come back on his promise.

"Queen Elsa of Arendelle! Of course! That was ages ago! No wonder I kept missing! This must be a fixed point in time!"

"No, wait, Sir, my sister is a princess, like me. She will be a queen, some day, but…"

"Of course, of course", said the man, suddenly serious.

He looked at her with a sad smile.

"I'm sorry, Princess Anna of Arendelle, I really can't help you with your sister, but I can promise it will get better. In… well, some years."

"Okay." Anna shuffled hesitantly, looking down. "Does that mean you don't want to build a snowman now?"

"Of course I want to build a snowman! Just you watch me! It will be the snowmaniest snowman to have ever snowmaned in snowmankind!"

The tall man plunged into the snow, flailing fruitlessly trying to grab it, and Anna followed him giggling.

Elsa jumped as she heard steps echoing in the corridor.

"I have to go, now, Miss", she said, leaving the room. "I must stay in my room. I hope you liked the frost!"

"I told you to call me Clara. And thank you for the frost flowers. They were great."

Elsa skipped quickly to her door.

"Wait" Clara called. "That's my friend!"

A tall man in a waistcoat had appeared. He saluted Elsa with a large gesture and a friendly smile, then opened the door of the blue wardrobe.

"Wait, Doctor!" Clara called. "I wanted to ask…"

"No, no, we are leaving now. No time. Bye, Elsa! We will meet later! And watch this, you will like it. You too will like it", he added, looking in the corridor behind the box.

Clara tried to protest but the man grabbed her and pulled her inside the box. Elsa watched with puzzlement the doors close behind them, wondering how they would both fit in such a tight space. Then a lamp at the top of the box suddenly lit up, as the strange sound that had drawn her out of her room began to echo in the corridor.

Under Elsa's amazed eyes, the box began to slowly disappear, becoming more and more transparent as the unearthly sound slowly receded. Eventually the last echo died as the box disappeared for good, revealing a little girl with strawberry blond hair watching with amazement on the other side.

Both sisters exchanged an awed gaze across the corridor. Then Elsa came back to her senses and ran to her room, slamming the door behind her.

Clara strode around the TARDIS console, reaching the Doctor who was rummaging in a box he had retrieved from a panel on the floor.

"What was that all about? This little girl needed help! Why the sudden leave?"

The Doctor looked up.

"I'm sorry, Clara. That was a promise I made a long time ago, but I got the time wrong."

"So now you are travelling to the correct date?"

"No. I had already been there, actually. It's a fixed point in time, I can't do anything about it." The Time Lord smiled. "But it's OK! It will turn out OK, and I won't have to do anything! At least… I think. Is that not cool?"

Clara frowned, unconvinced.

"Look!"

The Doctor had managed to find something among the mess stored inside the box, and presented it to Clara with a flourish. She bent down to look at it.

"It's… a little TARDIS… made of… glass?"

She reached out to touch it, then moved her hand away with a little cry of surprise.

"It's ice cold? Is it made of ice? How did it not melt?"

"I don't know!" beamed the Doctor. "Isn't it marvellous, not knowing?"

The Doctor placed the little ice TARDIS back into the big cardboard box.

"Was that… from the little girl who made the frost flowers?"

"Yes! When she is older… I should go check on her later, someday, now that I'm on the same page. I never thanked her properly for this little sculpture."

The Doctor put the box back under the floor and closed the panel, then jumped to the console and rattled his controls.

"Come on, let's go somewhere warm! How about Las Vegas?"

Elsa looked at the little flowers of frost forming on the window, spreading from her gloveless hand. Fractals, she thought as she watched the patterns form, trying to commit to memory the word she had learned to describe her creations. She had no idea if she would see this strange woman again, but for now she felt strangely hopeful. Maybe one day she would really be able to control her powers. In the meantime, there was no reason for not enjoying their beauty when she was alone and there was no one who she could hurt.

She was also relieved to have seen that Anna looked happy. And she was pretty sure that her sister had been playing in the snow. There had been some white powder in her hair that had not melted yet.

Anna was looking into the courtyard, at the curiously shaped snowmen they had built. The strange man had insisted each time to build a better snowman, as he said the last one looked like something he did not like. None of them had ended up looking like Olaf, however.

But Anna was happy. Partly because she had been able to play with someone else, even if it was a grown-up, although he really behaved like a child at times. But mainly because she had been able to see her sister, even for a few seconds. And because there had been a little half-smile on Elsa's lips, that had not vanished when she had seen her.