If you don't already, wear an crew-neck t-shirt undershirt under your dress shirt and tie. It may seem counterintuitive to the "cool off" advice, but it provides valuable function. When you do sweat (and you will) it provides wicking so you won't get pit stains and the sweat won't show on your dress shirt.

I say this from Dallas and I wear a suit every day. It works.

I sweat even if I ride slow - I tend to run hot.

I sit for 15 minutes or so when I come in to cool down, then I use a Fresh Bath Body Wipe (I know not very green) which looks like a large wipe, but with more moisture. I keep deodorant and a small towel at work to help freshen up. Since I have a buzz cut, helmet hair isn't an issue although helmet lines on the balding head is kinda funny for a couple of hours.

I have 2 hangers at work that I hang my cycling clothes on to dry.