Great observations! You sound like a specialist.
I've stipulated in this series of articles on the relevance of climate to human cognition, that practically every pattern has multiple causes. Indeed, the total cause of any event is probably unfathomably complex. So it's a matter of teasing out the most relevant or interesting factors.
I'm not a scientist, so my point here is the modest one of saying that climate might be one factor. In the first article in the series, linked below, I cite the evidence that cooler ambient temperatures are better for higher cognitive functioning. (Whether that ends up raising the internal temperature in the head is another matter.)
I'm not sure, though, I see much of a link between infectious diseases and autocratic politics. I argue it's a matter of sliding into the primitive default mode (the kind that evolved before the ice age), to avoid taxing the brain in hot climates since that brain must spend resources cooling the body's temperature (or trying to get better sleep, or avoiding dehydration and anxiety, as the research shows).
The asymmetry here is that cold temperatures can be negated with warm clothing, whereas you could be too hot in the Torrid Zone even if you're walking around naked.
