People did prefer living in colder areas before AC.

The arrival of AC meant there was suddenly a lot of very cheap land around cities that are extremely unpleasant without AC. This resulted in migration and a housing boom which drives up the economy attracting more people.

Sure enough, Wikipedia says the population in 1940 was only 65k (which is still too many, but whatever). I would still assume that AC installation was very uneven and a luxury at the time.