Just out of interest - are all the staff wearing thick jackets too?
It might be worth contacting the HSE to see if there is anything they could say that would help to sway the minds of the school...
The place I've just finished working in I had to have a Dr's note to not wear my jacket while moving around the school, all staff had to wear their jacket when not in an office or a classroom - stupid, stupid rule.
I was asked by one child if he could take his blazer off, my response was yes, and no one needs to ask again, in my class take your blazer off if you want.
There is no maximum temperature for people in HASAW but if you dig deep enough in the amendments there is a max temperature for computers.
Mind you the place I was at 12 months ago when we had wweather like this I had to actually remove an electric heater because an adult students had switched it on, I'd switched it off, she put it back on again.
I did tell her that yes she might be cold but she had arrived in college in a sleeveless dress with no jacket/cardigan and no tights so if she was genuinely cold she should consider wearing more appropriate clothing.