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The tires of a car are rubber and hollow so there is a lot of pressurized air inside the tire. As the car travels down the road and the tires rotate and make frictional contact with the ground, the air molecules inside are constantly in motion and making random collisions with the tire walls and each other. This increase in molecular collisions increases the kinetic energy of the air which in turn increases the temperature of the air. Also, the outer part of the tire is in constant contact with the road and the high friction coefficient between the two produces heat, especially at higher speeds. This is why the tires warm up with driving use. If you measure the air pressure in a tire when its "cold" prior to starting the car and then measure the air pressure again after driving at high speed for 20 minutes, you will notice that the air pressure increases by a few psi as a result of the heat.
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