So this is kinda just something I thought of that I'm done pondering over in my head. It makes zero sense to me why fans cool you down. I mean think about it, heat comes from the motion of atoms. That's not just an outdated science fact, right? So why would a fan, which just moves air, make you cooler when realistically it's making the air hotter by an incredibly small amount? So why doesn't a fan make you hotter?
Saying that heat comes from the motion of atoms is one of those statements that's correct depending on how it's clarified. It is possible, for instance, for something very cold to be moving very quickly. 'Heat' refers to a chaotic motion of particles, and thus is unrelated to most kinds of purposeful motions.
A person who is hot radiates heat into the air around them, based both on convection (the heating most people think about) and by thermal radiation (You are Radioactive Man! Sorry, it's slightly less thrilling than people make it out to be). If the temperature is in the 80-95 range and the air is still, this means you're surrounded by air that's picked up most of the heat it can from your skin, and by waving a hand fan you can move that air out of the way and replace it with new, cooler air. Now, friction both at the surface of your skin and the surface of the fan will increase the temperature of the air, but that is a very minute effect unless the speeds are absurdly high, and then you have other problems.
Now, if the temperature is above human core temp (98.6), using a fan is still refreshing, because you're very likely sweating. Sweat is water, and water likes to be free and evaporate into the air. This change of phase (liquid to gas) requires some amount of energy, and it also requires there be relatively little humidity (already present water vapor). If the air is still, your body will rapidly humidify the air around you, and thus lose the ability to cool via evaporation. By fanning yourself while sweaty, you feel much cooler (even if the air you're moving across your body is in excess of your core temp) because the phase change taking place on the surface of your skin is taking energy from your flesh.