OK.

Get a bus pass or more to a place that never gets warm.

There is no magic outfit that you can wear that will change how your body works. If it is warm, you will sweat with just the tiniest bit of exertion. If it is cold you will sweat with higher levels of exertion.

How long is your commute? If you have a wussy commute (5 miles or less) you might get away with putting along. If I did that on my 12 mile commute, I'd have to leave another half hour earlier. And even if I didn't mind getting up that early, the main reason I bike commute is the exercise and endorphin buzz that lasts all day. I wouldn't get this putting along at 12 mph.