Another thought I had: instead of using the rules as-is, instead resolve them based on how much heat is *generated* in a turn.
For example:
Hellstar. You ran and fired 4 ERPPCs that turn. 62 heat. You roll on the table, but with a +8 modifier. This is at least 10, so it loses 1 heat capacity, starting the next Heat Phase. Heat for the Hellstar then drops back down to 2.
Next turn, run, and alphastrike, you now have 62 + 2 = 64 heat to compare to the table.
Dragon, vanilla 1N. Fires all forward-mounted weapons and runs. 10 heat. Roll with a +0 modifier. You're unlucky and roll a 10. Heat capacity drops by 1 next turn. Also means that if you fire and run the next two turns, heat can have climbed to 11 when you roll; a +1 modifier.
If you use this change, you should ponder bumping the target number to 12 or some such; rolling a 10 or higher is a 1 in 6 chance, which is rather high. And the vast majority of 'Mech routinely generate 5-20 heat in combat.
Another modification to ponder is a -2 modifier to the roll if the heatsinks are Double strength. -3 for Clan, if you're feeling generous. Most DHS designs push heat that'll have them failing rolls almost every turn otherwise...
But maybe that's desirable. =)
Do note that just running around, and even modest Jump Jet usage wouldn't require a roll.
Paul