Writing a sequel to someone else's story

About a year ago I read Costigan's Needle, a science-fiction novel written by Jerry Sohl back in the fifties. It's a good book, has a good story and ends well, but it also has enough material for a sequel or spinoffs.

I can't help but turn over the continuing story in my mind -- with a transgendered element, of course -- but I wonder whether it's okay to pick up someone else's story in that way.

The copyright runs out in 35 years (I looked it up). The author died eleven years ago. He's not famous famous, but he's not an unknown. He did write for The Twilight Zone and some other screenplays.

I'm not going to wait for the copyright to run out, and I'm not silly enough to think I'm writing for "posterity". (I'm waiting for posterity to write to me first.)

So what do people think? Do I just say it's fan fiction? Should I leave it? I don't really need to write it, but I have the stupid reason of finding the title Costigan's Thread almost irresistible.