Presently (unless something snuck in when I wasn't looking), I don't think anyone is awarded (or punished) for damage done by critical heat levels. If you force destruction of a Novacat with several Inferno charges, for example, your reward (or punishment! D: ) is very little.
Proposal: As heat is inflicted, keep track of who inflicted the heat. As vehicle cools, subtract even amounts of heat from all owners for the vehicle.
Example, Mech in combat:
354 heat points due to pilot Bob using equipment (MASC, JJ, weapons)
276 heat points due to lava (perhaps owner is environment, or perhaps owner is pilot)
471 heat points due to Alice hitting with heat weapons (Inferno, Flamer, PPC, Firebomb)
75 heat points due to Charles incidental friendly fire with heat weapons
Mech cooling tick, loses 12 points of heat:
354 - 3 = 351 from pilot Bob
276 - 3 = 273 from lava
471 - 3 = 468 from Alice
75 - 3 = 72 from Charles
Total temperature: 1164, plus say 30 from environment = 1194
Heat damage inflicted on Mech, based on 194 critical heats. (Say, 100 damage total in the tick.)
Bob is penalized for 351/1194=29% of the damage
Lava claims 273/1194=23% of the damage
Alice is rewarded for 468/1194=39% of the damage
Charles is penalized for 72/1194=6% of the damage
Probably hostile heat needs to be given priority. Hostile heat = 468, accounting for all heat damage.
Alice is awarded 100 damage score (though if she had help from her own teammates, she would need to share points, based on proportion of hostile heat each inflicted). (Rewards)
Second priority, if there is heat remaining: environmental (score ignored? or reduced pilot penalty?).
Third priority, if there is heat remaining: friendly/pilot (penalties).
Perhaps the score penalties happen at a reduced rate, e.g., Lava penalizes pilot but only at 1/5th damage; pilot heat penalizes pilot but only at half damage; friendly fire penalizes perhaps at 80% (50%, 100%, whatever). (If Mech self-damage penalties are to be kept in line with Aero crashing penalties, which can come down pretty hard on the pilot.)