It depends on the finish. I have removed dents on very expensive guns which had an oil finish. I placed a wet cloth over the spot and placed a hot iron on the cloth forcing steam into the dent. They came out just fine. I defy anyone to point out where the dents were.
I don't think this will work with a finish such as the high-gloss on a Browning, for example.
Like birdogs said, it won't work on a Browning or similar. The finish has to be removed first, so be prepared to refinish the whole stock. For small dings it's not worth the effort because there will always be more show up.