Excellent point. Also it's too simplistic to speak about DA alone as temperature and pressure altitude have independent effects on turbocharged and turbine engines. Those engines will not perform as well at 6,000 feet and 40 degrees C as they will at 10,000 feet and zero degrees, even though in both cases the DA is 10,000 feet.

@@igclapp Agreed! That same decrease in air density responsible for our lack of performance will also reduce the capability to carry away heat! Cooling is a function of air density primarily, not just air temp. Most aviators don't stop to think that although the engine may be seeing sea level manifold pressure, because of the heat of compression it is not producing sea level horsepower due to decreased air density in the intake charge(which intercoolers attempt to solve). In fairness, he DID touch on the fact that extended climbs at Vy may result in overheating in a turbo motor, thus extending the climb because of the necessity to accelerate to cruise climb speed(reducing ROC even further) or even perform a step climb. Also remember that although your engine may be outputting something close to S.L. horsepower, it is not producing S.L.thrust. Your propeller is an airfoil, and in the same way your wing is less efficient at higher altitudes, so your prop is less efficient at converting that reduced H.P. into thrust.

When I was a 737 classic and NG dispatcher, the AC on/off was part of the takeoff calculation. Default calculated with it on but if performance was marginal it could be recalculated off along with a special flag on the dispatch paperwork. (It was actually all of the bleed air for the airpacks not just the cooling subsystem.).

higher temperature higher difference. at 10C/50F difference is ~1% for molecules and ~1% lower proportion of oxygen content.