Its even so that if you have a spare tire and you put pressure of say 65 psi in it , and then you put it under the car, and lower it to the ground, the pressure stays 65 psi.
Because this was theory wich I assumed and many others, I once did a test.
Measured the pressure of my front tire with about 1000 lbs on it , then jacked it up and measured again and the pressure was yust a bit lower.
Again jacked it up and mesured , let it down and measured , so 5 situations 2jacked up and 3 on the ground.
3 mesurements for every situation and during the proces the pressure lowered about 0.5 psi by the little air that escaped when pushing the measuring device on the valve.
So with zero lbs on the tire and 1000 lbs the pressure was the same.
Mayby at verry low pressures of say 2 psi there will be a difference but not at the pressures we use for tires.
The higher the cold pressure , the more highening up by the same temperature rising. A normal car tire about 4 psi ( the well known 4 psi rule) but a pressure in the tire at 65 degr F of 100 psi will rise about 10 psi , when going to a normal warm inside temperature of about 112 dgr F .
The higher pressure warm is taken into account , whenn determinating the cold pressure. The tire can have hold at least 1,5 times the pressure needed for the maximum load .
Also the valves maximum pressure is given cold at 65 dgr F, and a pressure rising by temperature risingnup to boilingpoint of water they are tested for.
Here a picture of a spreadsheet I once made to play with the temperature and pressure and see what it does to the other.
