Okra grows tall and likes the heat. But I wouldn't exactly call it a shade tree.

Do you like Figs?

Oh, I love figs, and I have a fig tree that I just planted about a month and a half ago on the other side of my house, but the space on the south side of my house is much smaller, and so I didn't want to plant something like a fig that has such an aggressive root system and can get so large in a five foot wide space, you know?
Okra would probably provide a good shade, but my wife isn't crazy about okra. She's from Cali, and hasn't really learned to appreciate all good southern food yet. :-) If I can change her mind though, I will certainly put that in consideration.

Thanks for the answer!

Sunflowers??? They can get up to 15 feet tall, like the heat, grow very quickly, have beautiful flowers and delicious seeds.