I suggest that you bring what you are most comfortable wearing. I, personally, love natural fabrics. I love linen and will, in summer, have at least one linen blouse and/or large over shirt. I have at least one cotton tee with me and always 1 or 2 cotton, tailored blouses. I do also use/bring Lands end modal tees, which only have some cotton in them, but they don't bother me so they add to my changes as well. Other than my jeans, which have a small percentage of spandex intermingled with the cotton, I wear natural fibers when on the airplane...as I'm a neurotic risk manager. ;) They do dry stiffer than man-made fabrics when washed/dried by hand/line, but I find they loosen up over the course of the day. Linen is fine wrinkled, although if I can I will touch them up, but that's just me. My cotton blouses, Jones of NY, seem to dry fine without needing ironing.
So bring what you are comfortable in as it will make you more comfortable when you are out and about all day, even in the heat.