Pulling this thread up to say thank you to it and others like it. I just picked up a bass on the used market and it had some fairly decent gouges on the back of the neck at frets one through three. They are a bit hard to see here, but my thumb finds them just fine:
The one circled was the smallest one. There were two or three others running for about two or three inches along the back of the neck.
Half an hour with a wet washcloth (folded in half) and a clothes iron on medium heat, and there is no trace of them! This is as close to a miracle repair as I've seen - especially for a do-it-yourself job.
One thing, though. The moisture can leave the neck feeling a little rough in places, so light sanding with a very fine grained sandpaper may be necessary.
Again, thanks for the tip! My bass would still have these neck gouges were it not for TB!