Your perception of temperature is largely governed by how quickly your body can shed heat. And how quickly your body can shed heat is related to the temperature difference between your body and the air immediately surrounding your body. The smaller the difference, the less quickly you shed heat and the warmer you feel.
Wind (or any other form of air circulation) moves the air that you’ve warmed away from your body and replaces it with air that has yet to be warmed by your body. This is why wind only makes you feel cooler if the air temperature is, in fact, cooler than your body.
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