GIna, I have several with very large leaves that do fine in our climate. One, called 'Lady Vanderwilt' looks a lot like 'Sophie Cecile' on steroids. I have had leaves reach 14". I have another whose name I can't recall at the moment, that has large leaves that look like taffeta. There are others with smaller but still outstanding colors and shapes out there, 'Don Miller' and 'Arabian Sunset' come to mind. I have had excellent luck with some of the rhizomatous begonias. They handle the heat well as long as they get plenty of light - but not full sun. Also, let them dry out in between waterings. They do best in containers for me.
Here are a couple of pics.
