Why pressure changes with temperature
Air in a sealed tire follows the gas law: pressure rises and falls with absolute temperature. The common rule of thumb is about 1 psi for every 10 °F. That's why your TPMS light comes on during the first cold morning of fall, and why a tire set to 32 psi in a warm garage reads 29 outside in winter.
Hot vs cold pressures on track
On track, tires heat far more than on the street, often to 140–180 °F inside, so pressure can climb 6–10 psi in a session. Most drivers pick a target hot pressure for their tire (the tire maker or series often publishes one), set cold pressure lower to match, then fine-tune after the first session by bleeding or adding air while hot.
Set pressures cold, at ambient temperature
For street driving, the pressure on your door-jamb sticker is a cold pressure: check it before driving, out of direct sun. Checking right after a drive reads high, and letting air out then leaves the tire underinflated once it cools.