If it doesn't bother him to rechange when you have to go back out, and as long as he can do it on his own (teach him to set his clothes aside nicely, so if he needs to change again he can wear the same ones), I don't see the problem. It's probably that he's very warm blooded, and maybe he will outgrow it.
Both of my children are warm blooded. We live in Minnesota. I am freezing if not fully dressed, WITH socks and a sweater, but the run around in their bare feet and shorty pajamas (although when we go out, I certainly dress them for the weather.)
I think if I were you I would allow him to wear t-shirts to school. If he's going to push up his sleeves anyhow, he might as well be comfortable and just wear the t-shirt. You could have him wear a zip up sweatshirt over his t-shirt that he can remove in the classroom, yet have handy in case he does get cold.
(I do want to second Gamma G's suggestion, because it's what I did with my oldest. She would always wear her t-shirts in winter, yet she'd wrap up in a blanket, and her nice sweaters and long-sleeved shirts never got warm. I did what Gamma does...started packing away the summer clothes during winter. My children do not have access to shorts, and I only leave out a t-shirt or two for days with tennis lessons. Their only option now is to go sockless, which they do every minute of every day unless we are going somewhere.)