Even here in Florida, I wear wool tops for much of my winter cycling and occasionally my Ibex wool knickers. When the temps rise, though, I generally wear something like this:
Cotton Fitness Tee
I know cotton is the devil in most cyclists' eyes, but this shirt is so lightweight and does such a good job of wicking perspiration, compared to the average cotton T-shirt, that I wear one of them on my rides well into June (I have three). I like that I can keep my forearms protected from the sun, too.

July and August are a different story--some days, even at 6 in the morning, it's already hot and humid. I'm still looking for a satisfactory alternative to synthetic fabrics for cycling during that time of year. Any suggestions are welcome!