Presumably it's going to be up near the temperature of the tyre, so around 100deg C I would guess. It's going to vary with heat soak i.e. the number of laps driven at race speed.
Indeed, the lag between the tyre changing temperature and the air inside doing so is what is being gamed by the teams. Heat it all up to get the official pressure. Let everything cool down a bit to cool the air and thus drop the pressure, drive gently on the out lap to keep the tyre close to the right temperature but without adding too much heat. Then make use of the time taken for the air to heat and pressures to rise during the qualifying lap.
During the race, they'll be doing something similar but playing with air temperature - blow in hot air, take the pressure, let things settle down, pressure drops a bit and you gain from the pressure drop on track. The tyre is then running slightly under pressure. We know this effect works because it affects road cars too. Rule of thumb is 0.1bar change per 10deg C change in temperature. So that's 1.45psi per 10deg C change.