Bid Time Return

Author: Richard Matheson

30-something screenwriter (sic!) is dying of a brain tumour and lives out his final days in a hotel, where he sees the photo of Elise, a famous actress from the late 1800s. He becomes obsessed and turns into a historical stalker; finds out everything he can about her (she was single and had an affair with someone while staying at this very same hotel in 1896), becomes even more obsessed and finally make a transition into some kind of madness, believing that he's the mystery guy. Which means, he's got to travel back in time to consummate their long-distance attraction. He finds a suitable method for doing the time-travel thingie (self-hypnosis) and off he goes. Elise appears to recognize him instantly when she sees him, and they proceed have a hot, passionate night in her room. Still, complication ensure, especially since the 'time-traveler' now believes that his future self is actually an illusion of sorts that he has to get rid of. And there's more. And in the end he dies, of course.