I've worn this:
It looks a bit ridiculous at times, but it was one of the few times I've been out and didn't get even a tan, so I fell in love. It can get warm when it's fully closed, but you rarely need it to be unless it's really windy.
I've also worn a normal ball cap with a UV buff for my neck and sunscreen in the sensitive spots. And I'd also recommend looking at a sun umbrella:
http://gossamergear.com/chrome-umbrella.html
They're perfect for the desert and not only block the UV but keep the air around you cooler. Not to mention the benefits when it rains, too. You can easily attach it to your backpack strap and not have to hold it.