They do, but they are regulated by the internal cooling system. We already have rudimentary cooling systems for Smart Phones, who's to say that 24th century phasers won't have superior cooling?Removable power packs hadn't occurred to me, I guess since I'm used to consumer devices that get charged when not in use, but you typically don't take the battery out. Of course a weapon is a different matter, though. And undoubtedly, with the science-y techno-wizardry of the future, power packs won't get hot.
Kor
I still think everybody should've had a few Type-1 Phasers in their pockets at all times.
Especially given that there have been more than a few random kidnappings by aliens within TNG era alone.