So, I'm sure for some vanguards, we just absolutely hate getting heat from boxes, when our equipment is fully maxed out. That's why I think it should be converted into cr or something.
Here's my ideas:
At the end of the elevator, depending on the amount of heat, gets turned into a small amount of crowns.
It goes to a reserve storage of heat which you can use later on for other weapons.
When your current equipment is maxed out, heat dropped from enemies and boxes are removed or sometimes replaced with crowns or pickups.
Heat is like "XP". Once you're "max level" in pretty much any game, you don't hunt for that XP anymore.
However, I am personally all for heat becoming a sort of "dungeon currency". Like, you use heat for various things within runs and it's gone the moment you leave.
Here's a thread I made not too long ago about how to make heat more interesting.