We know that higher star equipment requires more heat to level than lower star equipment. But how much more? Not sure if someone else has already gathered the data, if not hopefully this is a good start.

I equipped a 5* Final Flourish and a 4* Avenger at the same time and leveled them up to 6 and 7, respectively:
http://wiki.spiralknights.com/File:Heat-comparison-between-4-and-5.png

It looks like the 5* weapon levels at approximately 85% of the rate of a 4* weapon since they reached 6/7 at about the same time. So when the Avenger hits Level 10, I'm guessing the flourish to be around 8.5. I'm not sure if this would hold true though since later heat levels take more heat than prior levels. But maybe because it appears to be relative then 4* 10 = 5* 8.5? o.O

Perhaps we could get data for the difference between 1-2, 2-3, 3-4 star also.