72 degrees with very low humidity (hopefully from your dehumidifier) can be pretty comfortable. So, you really got lucky.
I had a similar AC failure 10 years ago, and had to sleep on the cool tile floor of a ground level bathroom, with the doors shut and the cold water shower running all night long to absorb the heat!
After one night, . . . I drove 20 miles to a Holiday Inn Express!
Heat as you have described it starts around May 1st and lasts until October 1st in many of the southern states.
Mannyrock