Columbia Sportswear Tamiami II is positively the coolest shirt I have come across, and I've tried many. This is 100% polyester and breathes like no-see-um netting. I use this for fly fishing because it is not very durable, sort of like a knit material, but it's not knit.
My next favorite is RailRiders Madison River shirt. It's like the Eco-mesh but with a collar and a bit longer sleeves. I like the fact that I can turn up the collar to keep the sun off the back of my neck.
Truth be told though, I prefer wearing wool for hiking, year round.