I wouldn't do this on the way to school/work, only on the way home because of the sweat issue (Texas).
I like the idea of working on my spin, I hadn't thought of that. Problem is, my preferred commuter is a fixed gear, geared 42x16. Maybe I'll take my SS MTB (34x20) a few days a week and practice high cadence.
Or maybe one-legged stuff on my current bike?
Mac