Deep south . . . in July? . . .
Best advice -- make sure the rental car's AC works well, and bring lots of sunscreen and plenty of fluids.
I do hope you understand the distances you will be traveling. True story -- some friends of mine had friends of theirs come from Germany, who did not quite understand the scale . . . They thought they could take a "day trip" from near St. Louis to the West coast.
<Edit> Quick check of mapquest shows more than 1800 miles and more than 29 hours in the car. </Edit>
rental car has AC <- Chevy Equinox
Distance is no problem. Last year we drove along Atlantic coast from France down to Gibraltar and back on the Mediterranean side up to Germany. Totally around 5500 km in three weeks. We Europeans like to travel by car. I don`t know how many British people come through Bavaria to drive to Italy or Croatia. But a are some. Or ask the Dutch - they take their cars and campers through half Europe.
But anyway, we are flexible, so we might stay at some places longer and drive less
