Why am I unable to sweat in the bad heat? F30, European, normal BMI

F30 slim/normal, a bit of hypothyroidism apparently, healthwise OK but sometimes pretty fragile out of nowhere. Like now. I went from a Mediterranean climate to a desert where the temps reach about 40C (~105F). My route was:

day 1: 0 elevation +25+30, day 2: 1700 m elevation +35, day 3-5: 800 m elevation +35+40.

On day 3 I started feeling unwell with skin/nose/mouth very dry and developed a terrible headache. It eventually subsided after hours of agony, water, electrolytes, and extra salt. The next day I spent in my room with A/C set to Arctic but it didn’t help too much as it was too hot outside and I was in a standalone small bungalow. I also noticed I was unable to sweat whenever I had to go outside briefly. The day after was also bad but bearable, no headache which was a plus, and that was the first day when I went outside for a couple of hours in the evening (+30+28). This was when I was first able to sweat (not from movement but from the heat, I was in an open car). My operating temperature is from -30-25 to +25+30. In this range I’m able to sweat and warm up as needed.

Already happened before at just 400m elevation (I think this is negligible) and +40 in continental climate (French pre-Alps). I had to do cold compresses and shower every 30 mins to cool off. My skin and especially my head would also get super hot to the touch as attested to by others.

Any ideas on why I’m unable to sweat in bad heat?

PS Put cardiac flair as this was suggested to me. My other guesses are thyroid which was kind of diagnosed before (hypo) but then refuted, or kidneys somehow.