Have you submitted fault reports through the official routes (i.e. not just by emailing building staff, unless that is the official fault reporting process)?
Is there an actual fault (i.e. the heating is stuck on, or there's air conditioning but it's not working) or is the building naturally absorbing and retaining heat and you have no way of getting rid of the heat?
Are other people experiencing this problem, or is it just you/your room?
I appreciate that you've said this is private halls, but it might be worth talking to your university's accommodation office to see if they can advise you. If you've done everything you reasonably can with the accommodation provider, the university might be able to contact them on your behalf.