Simply put, once your gear has reach the point where it is fully leveled or ready to level you have practically no use for any of the heat you collect.
I would like to add a new item/mechanic to the game. This item would be called "Heat Sink", it's purpose would be to sponge up extra heat and store it.
This stored heat could be used for various things.
With the stored heat you could use it to heat up gear in Haven or at an Arsenal Station, there would be a steep penalty reducing the effectiveness by 75% but you could use it to heat things without having to wear them. (also meaning you can craft up gear over 3stars without having to bind it and unbind it)
You could use it to craft Fire Crystals, or more appropriately you could use it to craft UP fire crystals. Any crystals you craft would automatically bind and would require more than what you'd get out of the current crafting DOWN system.
Evo Catalysts... these would be the most costly of all the items you could craft but it would cost orbs, stored heat, and Fire crystals.
As a very important side not the stored head would slowly decrease (cool down) and would require daily play to keep the stored heat increasing.
Feel free to offer your own suggestions on this and ask questions
I would say heating items would bind them to you. While selling would be nicer it seems this would disrupt a lot more than it would need to.
Personally I really like the idea of having heat be an in-run currency with several per-run only usages, making heat into something fun and exciting but temporary.