Whats wrong with cotton?
Surely you're gonna cook in even a thin wool shirt, pretyy sure i would
While its not a dress shirt, i actually like my wool tshirt best in summer. Wearing it now and it was 30C here today. Just a thin wool tshirt from icebreaker, and can't say i've been too warm (well, other than the normal 30C heat being much too warm for me, i can stand cold a lot better than heat).
Cotton is great for heat too, but it's just so uncomfortable for me since i sweat like a pig, and i really dislike the feeling of wet cotton.