Answer: Your body is producing heat at all times. This heat acts somewhat like an aura around your body, an invisible membrane between you and the air around you. So the temperature you feel on your skin is a combination of your own heat mixed with air temperature, and when a strong gust of wind hits you, it briefly strips you of that membrane.
This is also the reason why standing in 70F degree weather feels much warmer than jumping into a 70F degree pool of water.
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