Not true. Think of to the Bedouins in the Sahara, the Inuits in northern Canada and the tradesmen crossing the Silk Road since the first Egyptian empire. Or anyone in India for the last 7k years. Humans have been living with temperatures ranging from -50C to 50C for thousands of years.

The American southwest (i.e. Arizona) was thinly populated until the advent of air conditioning.

They had swamp cooling. Also the rivers actually had water in them above ground. But yes, less people.

Even in pre-colonial times? Or whas it just that Europeans settled in places that felt like home?

Like where? Early human civilizations started in some of the hottest places on earth.

Climate in the "Fertile Crescent" during the Neolithic was cooler and wetter than it is today.

And even today it is not really among the hottest places on Earth.

Houston