With a seven minute commute, I wouldn't worry so much about overheating and would just suck it up and get a high-vis vest. Another cheap solution for your signaling hand are these blinkie LED buttons Since you're going such a short distance, you could slap one on to your glove or sleeve and just keep it on for the whole ride. They have strong magnetic attachments, and while they aren't designed for cycling, when my husband bought some my first thought was "wow, I could cover myself with these and be really visible! And look like something from a Disney parade!"

This is something that's likely only going to be a problem for a few weeks each fall and spring. I used to commute into the sun like that and it was always horrible for a few weeks, and then it would get to the point where the sun was either high enough or low enough that visibility was easier.

Sarah