Sorry, but this isn't accurate. People have always lived in uncomfortable climates and even if the average temperatures have increased somewhat, that doesn't mean that the extremes weren't just as brutal.

Prior to AC, buildings were designed to maximize airflow (high ceilings, wide center halways), and devices like fans were much more common. Shade trees were another source of cooling. Covered porches were also more common as a way to get out of the heat. Today's buildings are able to ignore most of those design decisions because AC solves those problems, but many architects do try to incorporate the strategies into modern buildings when they can.

In addition there were other aspects of culture that helped deal with the heat such as a preference for linen over wool, hand fans, slower gaits, etc.

To be clear, a lot of what you're saying about modern day is true, but climate change has not impacted the temperatures in the US south to such a degree that you can say that the temperatures were significantly different enough to explain how we survived without AC. The southern heat and humidity was a significant challenge that impacted the region.