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In an ATIS or AWOS/ASOS recording, is the reported altimeter setting corrected for temperature?
I think it must be, because on a hot day, the altimeter should still show correct field elevation. If it wasn’t corrected for temperature, then the reported field elevation could be badly wrong on a really hot or really cold day.
(This and other questions describe pressure and density more generally.)
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.
The given sea level pressure from an ATIS will reflect the local deviation from standard temperature such that your altimeter (which does not correct for temperature) displays field elevation on the ground.
It is important to note that the ATIS/AWOS/ASOS station is directly sampling station pressure, not sea level pressure, which must be derived. The equation used to do this is the hypsometric equation and there is an assumption of temperature in the atmospheric layer between the ground and sea level.
$$(z_2 - z_1) = \dfrac{R\cdot\bar{T}}{g}\ln\left(\dfrac{p_1}{p_2}\right)$$
In this equation $z_1$ is 0 m, $z_2$ is station elevation, $R$ is the gas constant for dry air, $\bar{T}$ is the average temperature between $z_1$ and $z_2$, $p_1$ is sea level pressure (hPa), $p_2$ is station pressure (hPa) and $g$ is acceleration due to gravity. All are known except $p_1$ (assumptions about $\bar{T}$ are made from the lapse rate of the standard atmosphere and station temperature). Solving for $p_1$ yeilds:
$$p_1 = p_2 \exp \left( \dfrac{g z_2}{R \bar{T}} \right)$$
The altimeter is adjusted for air pressure, which is a function of temperature (and altitude). So the answer to your question is yes.
That is why it is bad for an airport to be "hot and high" (think Phoenix in the summer), the high altitude is compounded with nearly 100°F (40C) temps, makes for very thin air.
