It may only be a coincidence, but is not the amp cooled by the ECU fan output? Just sayin'.

I haven't yet heard of an OEM amp "overheating".

Are you using these:
Kappa 60.11cs - Infinity
@ 2 ohms? Maybe so. Though the Infinity Reference (2 ohm) I installed don't cause issues even trying to keep up to road noise.
Perhaps issues with the crossover?