One of the best places to see heat spots is on a manual transmission flywheel where the clutch has been slipping--lots of spots of varying sizes and usually in a circular size. If they are very bad or very numerous, replacement is necessary. Heat spots per se might not cause the grabbing of the brakes, but changes in the roundness of the drum can. Even new drums, if stored "un flat" in the box, might need to be trued up prior to use.
When refinishing any drum or rotor, the minimum thickness specs or max internal drum diameter specs must be heeded and followed. Also, the finish of the braking friction surface is very important too, especially with the newer metallic brake lining materials. If the finished surface is not to specs and, in the case of disc brake rotors does not have the non-directional swirl finish, initial braking applications can cause early fade and smells until things get broken-in.
Seems like there were some earlier drum refinish machines that ground the braking friction surface whereas modern machines are lathes. With a lathe, whether on a drum or a disc brake rotor, the finish results in a continuous string of fine grooves, much like a phonograph record. With metallic linings, the metallic particles will grab into the grooves like a phonograph needle on that record does, which can cause chatter and other noises until the friction surface is worn smooth. Hence, the need for the non-directional swirl on the rotors and probably some sort of regular finish grinding on the drums where semi-metallic brake linings are used. Just like in a paint job, finish prep is important and looks can be deceiving.