Is the altimeter setting corrected for temperature?
The reported altimeter setting, QNH, is 'somewhat' corrected for temperature, in that it corrects for temperature error at the aerodrome elevation. This is the main difference between the more-meteorologicaly-inclined QFF which does not contain this temperature correction.

You will still get altimeter errors because of the high/low temperature while being above (or below) the aerodrome  (about 40 ft for each 1000ft for each 10 degrees C), but the actual temperature error at aerodrome level will be 0.