Though the wiki has a page on heat, the information is fairly thin. Heat is hard to understand, because:

1. The scale is nonlinear. It takes far less heat to span levels 1-2 than it does to span levels 9-10.
2. Different star levels have different heat requirements.
3. Most importantly: doing controlled experiments is expensive.

Towards that end- and with the help of some overly trusting guildmates and an exploding block- I will try to amass information on how item requirements and heat levels compare. If anyone else finds themselves in the position of leveling more than one item at once, please, feel free to contribute what you know!

Sample experiments include:
a. Through careful leveling, get two items of the same star level to different heat levels. (such as a 4* item at exactly level 8, and another 4* item at exactly level 9) Heat them until the lower item reaches level 9. Then, we will know that for 4* items, filling level 8 uses __% the heat needed to fill level 9. (ASSUMPTION: items heat evenly within one level, so that the heat needed for level 9 to 9.5 = 9.5 to 10)

b. Get two items of *different* star levels at well defined points, and compare their heat requirements. Then, we will know how that 4* items require ___% of the heat needed to level 5* items, and that it takes ____x as long to level a 4* item to L5 vs a 3* item.

If possible, try to take screenshots and be as exact as possible. Make a note when your items overshot the target (like if a weapon filled levels 1, 2, and 3 all at once). This information could be useful in crafting, as well as in explaining what's a fairly unintuitive system.