Doesn't matter if you go up "X" thousand feet, or if the temperature thins the air out to be the same as that "X" thousand feet, the result will be the same on the engine. It's called density altitude, and that is what affects engines, and props/airframes as well. All full size aircraft manuals fully document this and give performance and fuel consumption figures for varying temps, altitudes, etc.

Just play with one of the density altitude calculators and you will see what I mean.

AV8TOR