I agree 100% with jackknife: LOOSE cotton is the key.
If you need quick drying and/or are doing high-aerobic activity, then the synthetic items are far superior.
But, the casual Columbia, REI and Ex-Officio shirts I have all feel hotter than cotton. Even the Coolmax t-shirts feel less comfortable--and itches, for some reason.
The only shirts I have that are compatible to cotton regarding heat comfort are my Pearl Izumi, Canari, etc cycling shirts, but those I have look a bit odd walking around town. There are some that are more casual, and I might have to look at them.
All of my casual synthetics result in a dry-feeling shirt, but I also feel sweat running down my body continuously (even the wicking shirts apparently have a limit). This is VERY annoying. The cotton absorbs some of the sweat, and I find that if the shirt is loose, and the temp warm enough, it evaporates ok. I have rarely had issues with a water-logged shirt sticking to me.
I was surprised by my findings, because being a former competitive cyclist, I always believed "cotton kills."
After visiting Disney World seven times (HOT and humid!), I learned that light-colored cotton works fine. Hydrate well.
I really like some of the synthetic shorts (the REI Sahara are nice) and hats (LOVE the Outdoor Research Sun Runner without the cape-thing), however.