I'm sure that everyone playing the game has, at some point, wasted heat. What I mean is, everyone has probably spent a little bit of time wearing entirely level 10 gear, so any heat gathered is irrelevant. So I had an idea to fix this.
The "Heat Sack" (Bag, Stone, Whatever)
It would work by acting as a regular 5* piece of equipment, gathering heat and leveling up to 10 (Or maybe only 5, to prevent it from being too useful). However, any heat gathered on the item can be redistributed to another item. The Heat Sack itself would obviously have no affect on stats/gameplay.