if you run your car with your climate control on AUTO, then yes, on hotter days the fan operation will kick in and turn at a higher fan speed(also RPM). Add to that the operation of your auxiliary fan, so yes... you might feel that "extra" rush of air u speak of.
I do not know about "reduced power" on hotter days, because the ECU dictates the optimum temp at which an engine should run(around 180 degrees farenheit) and adjusts ur fan speed accordingly in order to maintain that temp
Then consider a given... the laws of physics tells us that heat(over and beyond that optimum temp) will result in loss of power.
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