What makes Battletech plasma weapons cool is that they are hot. Since large craft don't track heat the way mechs and ASF do, capital scale plasma weapons aren't cool. The fact that they're more physically absurd the longer you want their range to be reinforces that lack of coolness.
True. You'd have to start making a second total for heat received in a turn, and require that to be handled by heat sinks the next turn.
The other option could be letting Plasma weaponry try for critical hits on enemy units. No damage, just chances for critting. Even then it might be a temporary effect due to the plastic plasma eventually cooling on the surface of a fire control radar, and not affecting it as much.
Of course if you manage to hit and then get a critical it on a fighter's life support with a capital plasma weapon, you have crispy fighter pilot.