I'm wondering.
Does it only increase when it levels up, or when creeps up the heat meter?
Like.... would a level 5 tempered calibur with half of its heat meter filled do more damage than a newly level 5 tempered calibur with only 1/4 of its heat filled?
If you look at your weapon's stats by mousing over it, you'll see a dark bar that is partially filled with color. This dark bar represents a weapon's potential stats. Whenever a weapon levels up, the color gets a little closer to filling the dark bar, at level ten, the dark bar will be fully filled. The color only expands at level up, not with ever bit of heat collected.
More of the mechanics of heat itself can be found at:
http://wiki.spiralknights.com/Heat
Hope this helps.
Is the heat you collect divided between all of your in-progress equipment, or does each equip gain the same amount of heat?
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I once attempted to figure this out when leveling a Striker for someone some time ago, while he leveled a Fiery Vaporizer Mk. II for me. I changed all of my other equips to ones that were complete.
Both starting and completing a Jelly run at the same time (not necessarily from Depth 9), the Striker was about 30% to Lvl. 5, while the Vaporizer was about 50% to Lvl. 4, if I recall.
I'm assuming he had other items equipped that were still in the process of leveling, so the contrast could be justified; on the flip-side, however, I remember health-reviving a few times during the run, and he may have been health-revived by someone.
Heat Collected is divided between all of your in-progress equipment, to state this in numbers, if you collect 100 heat and have two pieces of non-level 10 gear/weapons, each will obtain 50 heat, whereas if you have 4 pieces of non-max gear each will obtain 25 heat.
To answer your anecdote, unless you are in the same group, there's no guarantee you'll get the same amount of heat as another person as heat drops are random, but yes, revives and deaths must be factored in as well.
Not that I've tested this, but I'm pretty sure its per level. That would be too troublesome to constantly update a weapon per heat increment.