I don't see how riding 15 miles in the summer, Chicago if your location is listed correctly, and not sweating. I don't care how slow you ride, you will sweat. The only tips I can offer are this:
Get good cycling specific clothes that will help your body breathe, and avoid cotton at all costs.
Carry nothing on your body, no bags or whatever.
Leave the suits and dress clothes at work and change them out weekly if possible.
Have body wipes, deodorant, clean up stuff at work.
Give yourself extra time to cool your body temperature down BEFORE you change into that suit. <--this is huge! Do you have a private bathroom/office that is available to use? In the summer, I strip down, and just let my body cool down before anything goes on it. This is an ideal time to chug ice water and get breathing under control depending on how fast you rode.