Short and sweet is nice as well. Clearly stating your idea in a few sentences will mean more people are likely to read the thread to the end.

But I would rather see this item take up a trinket slot, and have a maximum amount of heat that can be contained. This would be heated as long as it is equipped, even if other items are being heated. Once it hits a maximum heat level, it will stop taking in heat. This means you can buy another container and grab more heat. Supply depot could sell these, perhaps at appropriate star levels (0*-5* containers) for prices up to 1000 energy. The contained heat will be enough to heat an entire item of that tier to completion.

This means if you make a new 4* item and have a full 4* container, and have quite a few shining fire crystals laying around, you can get the item to level 10 with even entering the clockworks with it!

An alternative function the item could have would be, at full heat, to be able to level up your item one level without fire crystals, but also without the leveling bonus. Maybe it has a high if not 100% chance of success, like 100% for 0*-3*, 90% for 4*, and 80% for 5*. This makes finding those radiant fire crystals not mandatory, but means that hours of grabbing heat will not ensure you get your item to level 10, whereas hours looking for radiants would have.

I think the idea you propose would be a great idea, but I was sort of piggybacking an expanded version of it onto the suggestion.

But I think sacrificing a trinket slot should be the way to do it. Or maybe have your battle sprite have a heat collection perk.