A space liner, with a large number of passengers aboard, is in difficulties while flying through the atmosphere of an unknown planet. Amy and Rory, who are honeymooning on the ship, appear on deck. Amy calls the doctor for help and the TARDIS soon appears ahead of the ship.
Meanwhile, on the planet below, Kazran Sardick, the richest man on the planet, is busy denying the request of a family to release their sister from cold storage. He had taken her as collateral for a loan. A servant interrupts with the news that the ship is about to crash, but Sardick refuses to send assistance. As the family is leaving, the Doctor appears in the fireplace.
He rushes to a control center to save the ship, but Sardick explains that the controls are isomorphic and respond only to himself. Appealing to Sardick's conscience does no good, but when a little boy hits him with a lump of coal, he refuses to strike the boy in return. The Doctor realizes that Sardick is not beyond help, bt rather is afraid of being like his controlling father.
Outside, the boy's father warns the Doctor that the fish that swim in the fog may be out tonight, and it could be dangerous. The Doctor provides Sardick with a video he had recorded in childhood of his father hitting him. In the video, his father leaves the room. Sardick tells the Doctor that that night he learned the most valuable lesson: "Nobody comes."
The Doctor goes back in time to the video and enters the room. Sardick, the child, explains that his father had invented a machine to control the cloud layer, but all he was interested in was studying the fish. They set up a fishing line in the fog to catch a fish, using the sonic screwdriver as bait. As a fish inspects the screwdriver a shark comes and eats both it and the screwdriver, and the doctor dives into a closet to escape. The shark breaks down the door but has the screwdriver stuck in its throat. The Doctor manages to retrieve part of the screwdriver but the shark can't survive outside the fog bank for long. The doctor and child-Sardick rush down to a cold-storage facility housing the "Surplus Population". The shark follows them and once again they have to escape. The Doctor releases Abigail who is able to sing the shark into calm. They place the shark in Abigail's cold storage unit and return it to the cloud bank. They then return Abigail to the cold storage unit, which has a counter on the front with the number 8.
The Doctor returns the following Christmas, and he and child-Sardick release her once again as the number drops to 7. This time they go on a sleigh ride through the sky, pulled by the shark. They continue returning to release Abigail each year on Christmas as the counter on her unit drops. Eventually Sardick is about the same age as Abigail. On that Christmas, Abigail asks to return to see her family and they all celebrate Christmas together. This time as they part, Sardick and Abigail kiss. Meanwhile, present-time Sardick is getting lots of new memories of the Christmases.
The following Christmas, Abigail explains to Sardick that she has a terrible secret, and Sardick decides that the Christmas visits are over. Abigail's counter has dropped to 1. Sardick's father perfects his atmospheric control giving the family control over the planet, and Sardick, bitter and angry still, rejects the Doctor the next time he appears.
In the present time, Pond appears to Sardick, pretending to be the Ghost of Christmas Present. She shows Sardick holograms of the people on the ship singing Christmas carols. Sardick remains obdurate and goes to visit Abigail's cold storage unit. He explains to Pond that Abigail has an incurable disease and has a single day to live. He has refused to release her for all these years in fear of her death. Pond brings him to the ship as a hologram where the crew appeals to him, still unsuccessfully.
As a last effort, the Doctor shows young Sardick his future self, the heartless and cold miser of the present. Repentant, Sardick attempts to save the ship, but the control console no longer recognizes Sardick as he has changed through the Doctor's influence. The Doctor comes up with a way to save the ship through Abigail's release. Her singing, amplified by the sonic screwdriver, stabilizes the atmosphere, saving the ship, and also precipitates snow from the sky for the first time in years. The final shot shows Sardick and Abigail enjoying their final Christmas together in the sky sleigh.