I don't know if the game does this (I've seen no indication) but when you're maxed out on heat, it goes nowhere!
I think there should be a Heat to Crown conversion, or divide the heat amongst the rest of the party (And if everyone is maxed, convert to crowns). The conversion rate would be to your (The developers) discretion, obviously.
Yeh, but what happens to it when you have nothing to put the heat in? Your other party members don't get the heat from you, because you end up with your share...so it goes wasted.
And what if no one has anything to put heat into? Then it's kind of pointless to be doing runs, isn't it? The point of runs would be to get crowns, so the heat would be totally useless, so why not have a conversion from heat to crowns. It doesn't have to be a very...game breaking conversion. They could set it to be 100 heat = 1 crown, so instead of wasting 1000 heat or whatever, you would end up with 10 crowns. Not much, but I'd take that over wasted heat, any day.
Well, heat is shared between the party anyway, so everyone has the same amount at the end of a dungeon run.