In "To Build a Fire," if you could go on from the ending, what would you say?If the story would not end, what would you say would happen next?
Obviously, any continuation of London's "To Build a Fire" is pure speculation, and you can extend the story in any direction you want without risking error.
I can give you a couple of directions you might want to take the story. A continuation of the story could center on the dog. London liked to write stories from the dog's perspective, so this would even fit London's practices. Maybe getting to the next warm spot is easy for the dog, but once its there, trouble develops.
Or, if you choose, you could probably pick up the story with the discovery of the body. You could then center on whoever discovers it.
Again, you can write whatever you want. These are just a couple of ideas.
Assuming that the man actually freezes to death in "To Build a Fire," I would also pick up the story with the dog's quest for survival. I would probably describe his journey back to civilization; how he might bury himself in the snow to avoid the much colder weather above; and then follow him to Henderson Creek, where the chechaquo's friends are waiting. I think this would be a satisfactory conclusion, but I suppose you could further draw out the story to show the men retrace the dog's trail back to their friend's body.