As someone who sweats a lot and works outside in brutal heat, I find the complete opposite is true regarding cotton vs polyester. Polyester wicks away the sweat and evaporates quickly, while cotton just soaks and turns hot, wet, and heavy.
I wish it were the opposite so that I could use less plastic overall, but I haven't found that to be the case.
Either way, a loose fit and complete skin coverage from the sun is essential.
I should definitely check out the varied cotton or linen weaves, then! I mainly wear a very light button down polyester for field work because of the benefits I mentioned and durability. I do a good bit of walking through thick brush and it's nice that it doesn't "pull" too much.