I don't have showers either. Here's what I do during the hot Summer months:

1. Shower in the morning. Put on lightweight clothing (gym shorts and sweat-wicking running shirt (C9 gear at Target is good and cheap).
2. Ride to work, taking it a bit easy on the hotter days. Usually it's under 80 in the mornings, so I'm not sweating heavily.
3. Once at work, cool down at the desk for 10-15 minutes, drinking lots of water.
4. Once cooled down, change in the men's room. Toweling off and an unscented wipe for the nether regions does wonders.

I haven't had complaints yet.

On the ride home, I sweat up a storm and shower when I get home.