I like ideas for repurposing but this has a couple of things that prevent it working. All will go as planed for a while and aside to problem you mentioned with t-stat,coils will begin frosting and soon ice over. Don't become discouraged,you are using your head and that's good.

and as the coils frost and freeze over they will soon melt and the water from that will run through the drain lines and pour all over your inside room and down the inside walls.