Unless you have very serious hills, you can ride in a manner that you don't sweat much more than walking in the same heat. I have a six mile each way commute in sometimes very hot and humid Virginia. Last year I did the whole wipes and change of shirt thing during some of the summer. This year I don't bother, and I much prefer it this simple way. I ride a tad bit slower in the morning. I get to the workplace about two minutes later, but I get to working earlier not messing around with all that. The alternative for my ride would be walking 10 minutes to and from the Metro (subway), so it isn't much different than that. I notice others who walk here don't change clothes after arriving. I carry a bandana to wipe light perspiration (or rain) off my face before I go in.

You may want to wear a Champion double dry t-shirt under your dress shirt. There are quicker dry button-down shirts as well, but they don't always look quite as nice. Rivendell Cylcles swears by light searsucker shirts. Yes, they are cotton. But really the best way to stay cool is with a billoway light shirt, not a tight synthetic one (regardless of it's wicking ability). You can also get can compression seamless quick dry underwear (like Champion Double Dry boxers). I use those sometimes. I also have a pair of quick-dry light nylon khacki pants that I got on sale at REI, but I normally wear normal pants.

In all but the hot times, get as much merino wool clothes as you can. They don't stink, and are much better with wet and heat regulation than most anything else.