I think there are steps that could help reduce the affects of heat. Things such as more street trees, less asphalt (reduce the heat island effect), heat reflecting building roofs, etc.
It's not like the south is a lost cause, improvement can still be made.
Chicago can (and in some areas has - along with Boston) fixed that issue with pedestrian tunnels that allow easy movement during cold weather. A similar fix is available for southern cities but I think a more reasonable approach is just tighter pedestrian alleys that prevent full sun from ever bathing the walking surface (and reduce sun exposure to buildings) along with lots and lots of trees. Trees are seriously amazing and dissipating heat from the sun.
Once you eliminate the sun you just need to make sure that wind alleys are set up to keep air moving through the city and have regular green spaces with water to help reduce air temperature. This can be done quite sustainably - Las Vegas is actually a great example of (rather) sustainable water use from a city built in the middle of a desert.
I lived car-free in Chicago for 7 years. I now live in an inner-ring suburb (Oak Park), car-light (my wife and I share a car that I drive as little as possible). If we define 15 minutes as ¾ mile walking distance, I have within that range, two supermarkets, a library, health clubs, coffee shops, two drug stores, dry cleaners, banks, doctors, dentists, schools, daycare and a number of restaurants not to mention a stop on the “L” and at least half a dozen bus routes within my 15-minute zone. If I didn’t prefer Trader Joe’s to a mainstream super, I wouldn’t drive to go grocery shopping (and TJs is just over a mile away). If I expand my range a bit more, I add in even more of all the above plus a book store and movie theater.
It's not like the south is a lost cause, improvement can still be made.