Er – strictly speaking, as regards the effect on the air spring, won't the spring rate go DOWN a little as the shock heats up?
Air heats up, and wants to expand.
So, for a given force on the bike through the shock, the shock will compress less. This means less sag when the bike's at rest – but the rate of increase in the force needed to compress the shock is a function of the change in volume of the air spring, not pressure at the sag point.
Less sag => greater air chamber volume => a more gradual ramp up in spring rate?
At the same time, whilst the sag is reduced as a result of the heated air, the load on the bike is unchanged and so the pressure inside the air chamber will also be unchanged. Just hotter and bigger.
I have no idea whether the effect is substantial in practice. One way to check would be to compare the sag at the end of a run with your normal set up.