I think this is definitely the type of challenge that everyone in the general population (not only us willpowering mustachians!) should impose upon themselves at least once in a while. It literally forces us to experience living out of our comfort zone. The reason I say this is due to the hedonistic adaptation factor mentioned by MMM that most people succumb to over time. My mother is a prime example of this. She is so used to controlling the temperature to suit her needs that she is unable to tolerate any temperature she considers too warm or too cold.
Despite being located in Ottawa, we do get hit by pretty intense heat waves, such as is the case these days. I manage, through various techniques, to keep the house relatively cool during these periods (unless they are extended ones) without using A/C, but I do admit to having turned it on 3-4 times last summer.
I understand, however, that some area in the U.S. the heat/humidity can be unbearable at times, though. I remember, as a young lad, having traveled to Virginia during the summer with my parents and I couldn't believe how people would want to stay outside for a minute or two given how humid and hot it was. The only two places we wanted to be was inside where there was AC, or in the Atlantic ocean's waters!