On a hot day, fanning yourself helps cool you down through convection.
Blowing the air across your face allows the air to pick up some of the heat off of your face and carry it away. This is what gives you the cool feeling on your face, even if the air itself is warm. When the air gets warmer going across the surface of your face it naturally expands and rises, being replaced with some slightly cooler air, to continue the process.
Sweating, or spraying yourself with a cool mist, assist in cooling yourself down through a mixture of conduction (the cool mist, or sweat, drawing heat away from the surface of your skin) and evaporation.
Edit: spelling.
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