I do nothing for minor burns, they seem to help build up calluses, but the reheating effect you mention certainly does get your attention
These days I have more problems with keeping my calluses thick enough to protect my hands but not so thick and dry that they crack. I can normally be found with one of my fingers taped with bag balm or whatever lotion is handy under it to "fix" a crack.
We have this little plastic scrubber at work that was made by GoJo (came with the handwash at some point in the past I guess) that Id very much like to get one for myself. It has three different lengths of stiff brushes from about 1cm long to just raised bumps. While I have pumice stones they clog up with skin cells too quickly to be really useful as your constantly having to clean the stone.