Since moving to Hawai`i, I try my best to stay away from suits. I can't find any that are breathable and allow me to stay cool. However, when I have to wear a suit, I generally carry the suit jacket with me until I get inside where there is air conditioning. I generally wear a sleeveless or short sleeved silk top under my suit jacket so it looks nice when the jacket is off. Of course, you'll want to find the summer suits that most high end manufacturers offer to maximize the lightness of the fabric.
My alternative is usually a pretty chiffon skirt (print pattern on top with light lining underneath). These are light and loose enough for air to circulate around my legs. The skirts also release wrinkles easily if you just hang them in the bathroom when you take a shower or with a quick steam of the iron. I top the skirts with sleeveless tops (anything lightweight) and usually a light matching cardigan.
I also see many women here wearing the Software sets which come in jackets, tops, pants and skirts. I have a couple of these pieces and they don't wrinkle and are light.
Recently, I've noticed more cotton with lyra blend jackets and skirts which look like they might fit your needs without the wrinkling of regular cotton.
TF