Kazran Sardick, a wealthy miser who owns most of the planet below as well as the cloud belt, reflects on the human tradition of celebrating the midwinter solstice. On this planet the settlers called it the Crystal Feast. He thinks that the whole concept is a waste of time and money. He has inherited a money lending business from his father and part of his practice is to cryogenically preserve members of any family who has ask him for money. He then uses them as security.
On Christmas Eve, he meets a poor family in his library. They have come to him to beg for the release of one of their family so that she can spend Christmas with them. She is a young beautiful girl, the sister of a middle-aged woman. Her chamber stands in the middle of the room. Kazran rejects them as a matter of course. Similarly, when the President of the planet phones to request his permission for the star-liner from Earth to land safely he refuses. He says that crashing is a kind of landing and is unmoved when told that there are over four thousand people on board.
The Doctor suddenly arrives, sliding down the chimney, arriving in a cloud of dust and saying that he couldn't resist a chimney on Christmas Eve. The family, still in Kazran's library are amazed witnesses as he tries to persuade Kazran to clear the ice clouds from the skies. The controls in the room turn out to be isomorphic and only accept Kazran's instructions. He refuses to help and says that he doesn't care if the people on the ship live or die. The family's young son throws a piece of coal at Kazran's head. The old miser goes to hit him, but holds back. He has the family removed. The Doctor, however, stays to confront Kazran. He says that he has noticed some things. The chairs in the room are arranged to face away from the portrait of Kazran's father. Although there is a Christmas tree in the painting there isn't one in the room. The Doctor concludes that Kazran does not wish to be like his father and the biggest difference is that he didn't hit the boy.
Outside, the Doctor talks to Amy over her phone. She tells him that the ship has less than an hour until it crashes. He tells her that he is working on a plan but is interrupted by a man who tells him that there is a fish warning. Looking up, the Doctor sees some fish swimming through the fog. When a Christmas carol is played over public speakers he suddenly thinks of a plan.
Kazran is sleeping in his chair in the library when a film is projected onto the wall of his twelve year's old self when he tried to film his first meeting with a sky fish. Kazran wakes to see the part where his father comes ranting into the room and strikes him for going against instructions. The twelve year old argues that fish like people, particularly when they hear singing. The Doctor appears in the room, saying that he found the film on an old drive. He asks if Kazran saw the fish; the old miser replies that it was the occasion when no one would come and he was on his own in the world. The Doctor leaves through the door and promptly reappears in the video, coming in through the window. The adult Kazran argues that this didn't happen before remembering that it did.
The young Kazran and the Doctor are hiding inside Kazran's wardrobe. The Doctor has hung his screwdriver in the room and left the window open to lure the sky fish in. Kazran tells the Doctor that he is the only child in his class who has never seen a fish. When the Doctor peeps out of the wardrobe door he sees a small fish playing with the sonic. The Doctor is curious and steps out, despite Kazran warning him not to. Almost immediately, a large sky shark swims in through the window and eats the fish and the sonic screwdriver. The Doctor manages to get back into the cupboard where he tells the boy that he has learned how the fish swim in the fog, which will help him to land a space ship in the future. The shark smashes through the door but gets wedged in the frame and the Doctor reaches into its mouth to retrieve the screwdriver. The shark has bitten it in half. The Doctor manages to use what is left of his device to stun the shark but, out of the cloud layer, it begins to die. The boy is aghast. The Doctor says he needs a life support to get the shark back into the sky. Little Kazran offers him an ice box. They run through the house to a chamber full of cryogenic suspension units. Unfortunately, they cannot open any of them without a code. Back in the future, the older Kazran is vainly shouting the code at the video of these events. The Doctor reappears behind him, hears the number, and goes back in time to open the door.
The box contains a young woman called Abigail Pettigrew. Her video message relates her love of fish, which they take as permission to borrow Abigail's box for the night. The shark has followed them to the vault, homing in on the half of the sonic not in its stomach. Before it can attack, Abigail sings to it, calming it so that they can place the shark inside the box and the three of them take it into the TARDIS. They return the shark to the sky. In the future, Kazran turns to look at a picture on the wall of his library: it is of Abigail.
The Doctor notices a dial set at eight on Abigail's ice box. He asks her why but she replies by asking if he is one of her doctors. They take her back to the vault but before they shut the box the boy tells her that the Doctor has promised to return every Christmas. Every time the door closes it seems to Abigail it reopens with the Doctor and Kazran wishing her a happy Christmas. The Doctor takes them out on excursions: the first is a shark-drawn carriage ride through the clouds, later he offers them all of time and space. The older Kazran can be seen, looking through a whole pile of photographs of these adventures, wondering how he can have new memories. However, after each visit, the dial on Abigail's ice box counts down, moving from eight to two.
Eventually, Abigail sees that Kazran is older than before. She finds the young man attractive. She asks that this time they visit her family. Watching her relations prepare for Christmas through the window she begins to cry. Kazran asks why and she says that she is watching the life she will never have. They go inside and Abigail's sister invites them to have dinner. She warns her that Kazran will turn out just like his father. On their return to the chamber the young couple share a kiss.
The following Christmas the Doctor takes them to a Hollywood party. Kazran is upset when he finds Abigail crying by the pool. She tells him it is time for him to learn the truth. The Doctor finds them kissing: he wants to leave because he has accidentally got engaged to Marilyn Monroe and a car is waiting to take him to a chapel. When the Doctor and Kazran return Abigail to her box the Doctor tells Kazran that he'll come back in a minute, changing that to "next year" but Kazran says Christmas is "old" and he doesn't want to do this anymore. The Doctor is puzzled that he has failed to change Kazran and gives him the half sonic screwdriver in case he needs him. Kazran replies that he won't. Abigail's dial has turned to one.
Christmas Eve, a few years later, Elliot Sardick shows his son the completed machine: the sky and all that is beneath it now belong to them. Kazran goes up to his room and looks at the screwdriver. He turns and sees the Doctor standing outside his window but he shuts the curtain and puts the screwdriver back in the drawer.
The older Kazran again refuses the president's request to open the cloud belt and let the star-liner land safely. A hologram of Amy appears in the library. She says that she is the ghost of Christmas present. She tells him that she has brought him something. He hears singing in the vault: the ship's passengers are singing "Silent Night", singing for their lives. Amy tells him that they are trying to control the clouds with their voices. Amy tells him that the Doctor was trying to turn Kazran into a kinder man. Kazran says that time can be rewritten but people can't. He stalks angrily through the hologram choir and they blink out of existence. He stops at Abigail's ice box and tells Amy that Abigail was dying when she volunteered to be frozen. She only has one day to live. He asks how it is possible to choose which day to let her out. Amy apologises and then projects a hologram of Kazran onto the ship's flight deck. He sees the crew vainly trying to control their descent. He replies to their pleading that everybody must die some time.
Back in the chamber, the Doctor says that he will now show Kazran his future. Kazran says that everyone dies cold alone and afraid and nothing can change him. He says that the reason he won't help the ship is because he simply doesn't care. When he demands that the Doctor show him the future he realises that it is already happening: his twelve year old self is there, witnessing all of this. The boy at first confuses his older self for his father who goes to slap him. As the memories of this pour into him he hugs his younger self and he decides to save the ship.
There are only five minutes to save the ship. The problem is that Kazran's brain waves have changed too much and the machine no longer responds to him. The Doctor thinks of a new plan. Using the half of the sonic screwdriver he will signal the other half in the shark in the clouds. He needs to release Abigail because her voice resonates with the ice crystals and can calm the sky. Kazran releases her. She chides him for waiting so long but tells him that they have shared so many Christmas Eves and says that it is time for them to have a Christmas Day. She sings and the ship's crew land the ship safely.
The skies have changed and snow begins to fall. Amy and Rory meet the Doctor in the street. Amy asks where Abigail and Kazran have gone for their last day together. A shark-drawn carriage passes overhead.