I bought a peony at the Birmingham Botanical sale several years ago. Planted in the ground in full sun with no problems! I have found mine to be very tolerant of heat and requires very little maintenance. It may depend on the variety you select, but I haven't found heat to be an issue.

What I have found with my peonies is that they must have good air circulation. I think the problem in this area is more likely to be humidity than heat, so be sure to plant them where they won't have anything tall growing close by.

Peonies need between 100 and 400 hours of cold weather under 40 degrees to properly set buds. These are a list that need less chill hours:

Da Fu Gui�/ �Great Prosperity�
�Lian Tai� �Budda�s Lotus Seat�
�Qi Hua Lu Shuang Mrs. Frost �
�Shan He Hong� Red Mountain and Red River
�Gold Dotted Red�
�Festiva Maxima�
�Paula Fay�
�Cytherea�
�Red Magic�
�Sarah Benhardt�
�Shirley Temple�
�Sword Dance�
�Yang Fei Chu Yu�
�Fen Yu Nu� �Pink Jade�
Fairy Princess
Abalone Pearl
Miss America
Zhu Sha Pan � Red Cinnabar
Fen Pan Cang Zhu � Red Pearls in Pink Tray
Pan Tuo Rong Hua- Narrow Petal on Plate
Tao Hua Huan Cui
Purple Jade Zi Fen Yu
Snow on Peach Blossom Tao Hua Fei Xue
Beautiful Wrought Jade Qiao Ling
Garden Pink Zhao Yuan Fei
Bright Sunshine Qing Wen

They have quite a variety of peonies at the Birmingham Botanical Gardens and they are lovely. They are planted in partly shaded/dappled sun areas.