I keep cool with a constant 16 mph breeze. Any sweat I generate gets evaporated and keeps me comfortable in 75+F. But if that stoplight or stop sign is longer than 3 seconds wait, I'm soaked. And as soon as I get to the office I start sweating.
For the OP's 15 mile commute, just try it a couple of times. My commute is 13 miles, but I often ride 14-16 on the way to work. I change clothes when I get there, dry off any sweaty parts, splash water on my face and arms, and apply deodorant as needed (often reapplying after walking a bit at lunch).