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.
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