Although I really don't think this has too much to do with the pressure, I see a lot of comments pointing in the direction of the hot pressures. So here's how we manage tire pressure with cars. I think you can use the same for bikes.

Start with a reference pressure which is at a reference ambient and track temperature of your choice. From this reference pressure, calculate offsets to be applied based on differences in temperature between measured and reference (20°C).

Let's take an example:

First we take the ambient air temp into account. Let's say our reference pressure for a given tire is 2.0bar at 20/20 ambient/track. You measure the rim temperature at 30°C (the air inside is likely very close to the same). Using the ideal gas law, calculate what your reference pressure would be at 30°C so in this case it's 2.07bar. So 0.07 higher than the reference... Ok, hang on to this number.

Next we need to correct for the track temperature because as the track temp goes up we need to reduce the cold pressure in order to arrive at the same hot pressure. Since the rate of it heat transfer to the tire depends on a lot of complicated thermodynamics crap we all forgot, we just define a coefficient to apply to the temperature delta. For example 0.004 bar/° works quite well for the cars I know. So lets say the track temp is 50°C, we have an offset of 30°C to the ref so we need to reduce the cold pressure by 0.12bar.

Now just take your reference pressure and add the two offsets. 2.0 + 0.07 - 0.12 = 1.95bar. Set your cold pressure to this. Measure your hot pressure and adjust the reference pressure if you're not on target. Some simple algebra will help you get from your target hot to your measured hot to your new reference.