Hot and cold for me I don't think is a trigger however I have a bototm cracked molar. We are crowing that in two weeks. When cold hits it, I get pain. We were thinking referrred pain perhaps however most of the time it is just the upper teeth aching and pushing on the gums when it's flaring hurts. Yours sounds more trigeminal. My doc wants me to get a brain MRI. I am waiting due to covid. If hot sun is triggering your pain on your check, it sounds like a nerve issie. Have you seen an orofacial pain specialist?