It's been awhile since I wrote anything on this and have picked up a few new ideas that may help you guys, especially the HPDE folks.
When you run your car, you will determine the best operating pressure for the tire, you may use the manufacturer's recommendation, or simply tried and true experimentation to get this ideal pressure. In any case, the first thing you must do is determine whatever pressure that might be...let's say you particular car handles like a slot car at 32 front, and 30 hot rear as an example..(always hot pressures, cold doesn't mean squat)
The next step is to determine how much pressure increase there will be from hot to cold, so in the morning, when the air, the car, the track, the tires, all of nature is at the same temperature, write this number down...lets say it's 70 degrees.
Set your tires at..(whatever, pick a number) say 26 front and 24 rear, and go run the car.at least 6 laps, and by that I mean run the crap out of it.
Come in, hot, and hopefully you picked a spot on pit lane close to pit in. Take the tire pressures. Let's say they read 36 front, 34 rear, so you bleed them down to 32F and 30R.
So subtract 4 psi from the front and 4 psi from the rear. (cold pressure at 70 degrees)
This should give you the following info
70 degrees cold starting pressure is 22 front, and 20 rear. This will be your new starting pressure at 70 degrees.
Let the car sit overnight for the next day and if it's another 70 degree day, you have your starting pressures..done.
If it's not a 70 degree day, then you have to decide how to make it one, and this is different from the way it was done before, that method was based on volume only, this is based on temperature if it's a 60 degree day, you might want to add 1 psi all the way around, if it's an 80 degree day, you may want to subtract 1 psi from all the way around. this is not the value that I use in particular, it's based on several different factors, but it will get you close, it has taken me years to develop my method of doing this and I received very little help from engineers along the way, so I had to figure it out on my own. If you keep accurate records, you can do the same
The biggest mistake I see is guys going back and trying to adjust the air pressure during the day, you cannot do this, once the sun comes out, once the car is started, even if the tent flap is up and one end of the car is in the sun, you are done, you cannot establish another baseline. You can adjust hot pressure, but never never never ever never go back to a cold pressure setting.
So run the car, and bump up or let down pressure to maintain that 32F 30R hot pressure, you should only have to go up or down less than 1 psi after you get used to this. All 4 tires will probably be different depending on the amount of right and left hand turns, don't worry about it, just get them to your 32/30 hot target pressure and don't worry about it.
At the end of this exercise you should now know the following info..
Cold pressure at 70 degrees
Hot pressures at "X" degrees during the day
Rate of pressure increase from cold to hot (this should be relatively constant for each corner)
The difference in rate of pressure increase from right to left, front to rear on this particular track.
The new cold pressure at your starting temp...using the 1 psi/10 degree factor whatever that staring temp is.

So the next day, you should be able to duplicate the pressures without much guess work.

Let the questions fly..and BTW these are not our actual tire pressures that we use.