It's very frequently repeated on Mumsnet that having bare legs and arms makes you hotter than being covered up from wrist to ankles in cotton or linen (in judgy threads about what people are wearing to the office or out and about).
If you are actually directly in the heat of the sun, then I expect white or very light-coloured fabric will cool you a bit by reflecting infrared heat. And covering up in the sun is obviously a good way to avoid sunburn.
But AIBU to think that it's complete nonsense if you're hot and inside or you're outdoors in the shade? We cool down through air movement next to the skin to allow heat loss and evaporation. So having bare arms, and bare legs, and/or a loose dress really does help. And men who want to wear shorts rather than trousers on a hot day are being practical, not unreasonable.
Caveat - men walking around bare-chested may be cooler but I don't care, they should put a t-shirt on anyway!