Should I quit this job because of the air conditioner...?

You are right and you need to contact a person who can take this further. I suggest that you go to the boss and explain that if this problem doesn't get resolved your going to your doctor due to ill health and you will get a solicitor/lawer also. If he doesn't turn it off then take it further. This is NOT allowed there are laws where you have to have certain temperatures in the work place.