I propose a system wherein a player's excess heat upon stepping on an elevator has the capacity to coalesce into a crystallized formation--Fire Crystals--dependent on the Tier, Stratum, and amount of heat the player finished the level with. (T3, S6 would grant a maximum of ~3ish Radiant Fire Crystals if a player finished the level without the heat going towards anything.
Crystals earned would be bound, and of relatively low amounts per-level, providing an incentive to run many levels in order to recieve something other than Crowns as a reward.
EDIT: This mechanism is best suited to the Arcade specifically, rather than Missions that take the player to a certain Tier or Stratum automatically, such as King of Ashes.
Perhaps heat can be condensed at arsenal stations or subtowns? I'd say make the final floor of King of Ashes not able to change gear in to avoid issues there, but doing this will remove the whole "boss missions are better now" issue.