The fan pushes the gas molecules to move faster in a single direction, and that speed increase is very small compared to the increase of the molecule speeds of a temperature increase.
The fan air cools you by two ways, 1] carrying away more heat because the air is already cooler. If the air is hotter than body temperature it will heat you up faster. 2] if you have sweat on your skin, it will carry away more sweat, which uses body heat to evaporate more sweat and cool you down.
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