Because body temp is a function: Temperature (T) equals heat gain (G) minus heat loss (L). T=G-L. If you want to cool down, you need to make L > G.
G includes things like: sunlight, heat absorbed from warm air, heat produced by your muscles.
L includes things like: evaporative cooling when moving air blows across sweaty skin.
Adding a hat (assuming you mean a ballcap or a brimmed hat, not an insulating winter hat) blocks a certain amount of heat input from the sun (*insolation*), thus decreasing G, and changing the balance in that equation. It *might* reduce some heat loss from your head, but as long as it stops more incoming heat than outgoing heat, it’s still a net reduction in the value of T.
Some hats actually trap heat in your body because your head is one of the biggest exporters of heat that you have. But, they provide shade to your face/ears/shoulders depending on the bill style that has a net cooling affect.
Trapping heat is why a lot of hats are actually mostly mesh or made of a hole filled material like woven reeds.
If it is extremely hot outside, keeping the sun from hitting your skin plus, your body sweat will create a natural barrier in-between the clothes and your skin which will be cooler than the extreme heat outside the clothes. This is why many desert dwellers cover themselves up completely. It insulates and because the body (although the human body can get hot) it won’t be as hot as the 110 degree weather outside.
Shade, they create shade.
Loose fitting and light colored clothing is the best for this.
The loose fit allows air flow to keep you cool and not trap heat. Wide brimmed hats are amazing at this, because they provide a lot of shade without actually tapping much heat.
The light color is important because that means it reflects, rather than absorbs, the sunlight that’s hitting it.
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