I suppose this angle has already been fully discussed earlier in this thread ... but have you considered that it might be a transmission problem ... since cooling of the transmission loads the main engine's cooling system?
For some reason, the tranny may be creating way too much heat. I have no idea what could be wrong internally with an automatic transmission to make it do this ... maybe constant excessive slippage in the torque converter - not excessive enough for you to really notice a pulling power problem - but bad enough to raise temps just enough so as to overload the main system's cooling capacity when traveling in raised outside air temperatures.
By the way, I would be more concerned about the excessive cooling system temperatures burning the transmission fluid - versus damaging the engine.
