Linen is definitely under-rated. It's nature's underarmor. Except polyester always seems to smell eventually because of how it absorbs sweat-stink, unlike linen. I'd definitely buy a white linen 2 piece suit, or just the pants if I find a deal. If I found not-expensive linen boxers them I'd buy them too. Linen sheets in the summer are also unmatched but expensive, and you have to iron them if you don't like a sloppy bed.
Thin merino wool socks are also pretty good, but usually I buy a merino-poly blend because it's cheaper and they're less likely to get stretched out of shape.
I also got some seersucker (which is a textured cotton) shirts which I'm excited for, and are supposed to keep you cooler because the texture creates less contact between fabric and skin, but idk about that in reality, i just like the texture.
I have no idea if rayon is actually good or not for heat.