What I remember from the novel:
The protagonist somehow gets transported to a different planet (I thought into some smaller object that happens to have a world in it). He starts out on ice where he has to be saved by the natives from the encroaching fire (natives have sleds to stay ahead of the fire). As the protagonist moves farther away from the fire, the land becomes warmer and greener and the civilizations more stable. Alternative world seems to have mainly medieval technology.
The song "Ring of Fire" by Johnny Cash was quoted more than once in the book. I think I read it quite a while ago (before 2000) from a library so I'm thinking the book is probably written in the 80s or earlier, but I might be wrong.