After a tyre has been on the road for a while, a pressure gauge often reads higher than it did before departure. The tyre has not somehow gained air. Repeated flexing, contact with the road and heat from nearby brakes warm the rubber and the air inside it.
As an approximation, when the amount of air stays nearly constant and the tyre’s volume changes only modestly, absolute pressure rises roughly in proportion to absolute temperature. Warmer gas molecules move faster and strike the tyre wall more often and with greater momentum, so pressure increases. “Absolute” matters here: an ordinary gauge reports pressure relative to the surrounding atmosphere. Atmospheric pressure must be added before applying a temperature ratio, so multiplying a Celsius temperature by a gauge reading is not valid.
A real tyre is not a rigid container. Speed, load, road conditions and weather all affect its temperature, so the model explains the direction of change rather than prescribing one fixed increase for every car. This is also why the pressure specified on a vehicle placard or in its manual is normally a cold-tyre value. The US National Highway Traffic Safety Administration defines a cold tyre as one on a vehicle that has not been driven for at least three hours and notes that a warm reading contains extra pressure. If a reading just after driving is above the cold specification, air should not be released merely to force the number back down. Follow the vehicle instructions and check again when the tyres are cold.
Source: https://www.nhtsa.gov/vehicle-safety/tires
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