You didn't give us much to go on, but it is possible that you are remembering Larry Niven's short story: "Wait it Out."
As the story opens, the first-person narrator is already trapped on the surface of Pluto. The extreme cold has put him into a form of cryogenic sleep -- when it's "night," meaning the narrator's part of the surface is turned away from the sun, his body is essentially at absolute zero as I recall, and he is completely oblivious to what's happening around him.
Whenever that bit of Pluto is facing the sun again (technically "daytime," although it doesn't get very bright when you're that far from the sun), he warms up just enough for his central nervous system to function at a minimal level. He can see what is happening in front of him, and can think about it. (He can't so much as twitch a muscle, however.) But it's his calculation that he is thinking and perceiving things very, very, very slowly -- so slowly that he may be able to "wait it out" until, several years from now, a rescue ship might finally show up from Earth to try to recover and defrost him.
So you could say that the terminator line is important to the plot -- the only times when the narrator is capable of thought are the times when the planet has recently rotated to put the sun "above the horizon" again.
You mentioned that there may previously have been another person on this planet with the main character. In "Wait it Out," we learn the narrator had been one of two astronauts who landed on Pluto. When something damaged their landing vessel so they couldn't take off again, the other guy opened up his spacesuit helmet as a means of committing a quick suicide. But the narrator decided that if he stripped off his suit entirely, very fast, he might be preserved (rather than simply killed, as you or I would expect) by the extreme cold.