I have this problem too, but we live in New England. I think that if I were in your climate, my children wouldn't own anything but shorts and tee-shirts because that's what they're wearing here. My FIL and husband run hot as well. My rule here is that my teenagers can wear what they want (in terms of warm or cool) and if they choose to freeze or look like idiots, they're free to do so. Many teenage boys here wear shorts to school all winter and no child over the age of 11 will be caught dead wearing a jacket any warmer than a Northface fleece.
With my younger boys (5 & 7) I put away most of their shorts after Halloween. It was probably in the 40's or 50's most days by then (although it's been warmer since then). Even on mornings as low as 30 (when it's in the 40's by recess time) they wear only a hoodie, no jacket. I'm not worried about them getting sick - viruses and bacteria cause illness, not how warmly or cooly they're dressed. When it gets truly cold, they will wear jackets, hats and gloves without a fight.
I say let your son decide within reason. Don't turn it into a power struggle or he will let himself be cold and not admit it. If you make it not a big deal, he'll just listen to his body. Perhaps make him pack a light jacket but not wear it, and send him to school in pants if it's below a certain temperature (65 maybe?) if you feel like people will think you're a bad mother. My kids' teachers know that I have and offer appropriate clothing and they choose to not use it, and they have kids like this in their classes every year.