Currently if you have all your equipment upgraded heat is useless. This is a bad design decision as heat is a reward only SOME of the time (actually more often it's NOT a reward than it is). Something needs to be done to use up heat.
So what I thought of is that each character gets a "skill slot". You could buy skills from NPCs for crowns/energy/whatever. Maybe you could get recipes for them. Maybe they could drop rarely from monsters. These skills would require a certain amount of heat (to be determined by the skill; better ones should require more heat) and would use up the heat when the skill is used. There could be a variety of skills like one that instantly creates spikes around you damaging any enemies near you. One could shoot out fire trails randomly from your body. One could be those hibernate shields that the gremlin mages use that stops you from doing anything but protects you and heals you.
Of course this brings up an issue of how heat is handled once you beat a level. I think you should maintain all the heat you've gathered from level to level (and lose it once you leave, much like the powerups). This would also encourage players to rez before the next level so that they don't lose their heat. IF you have gear that can be upgraded there should be a window that pops up after you beat a level if you want to keep your heat or deposit it into your equipment. That or make it so your equipment automatically gains the heat like normally but it doesn't drain it from your total reserves.
Actually, now that I think of it, a better alternative would be to just remove the function of heat upgrading your equipment altogether. Make heat solely about skills. Then just make it so that every monster that is killed while you are on the map gives you upgrade credit. Boss type monsters could give you more credit. Then make it so that your equipment can level while you're in a mission and not just at the end. There would have to be some sort of feedback mechanism to show that an equipment leveled (maybe have some white text near the top middle say "[equipment] Leveled!" for about 2 seconds then disappear).