when air is compressed it heats up because the uncompressed air contains heat. Heat is a form of energy that's all around us even in the coldest winter. Cold is void of heat, cold is caused by the lack of heat energy. That being said, when you compress air containing heat, the heat is also compressed. This causes the tire and the air inside to be warmer that the surrounding area till the heat is dissipated to the surrounding area. The tire and it's air inside becomes the same temperature as the surrounding space. Just remember, heat is a form of energy.
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