In warm/hot weather a hat, a bandanna, and a few other things are great for the desert environment.
Soak a bandanna with water and tie around your head or neck for cooling. Some have even responded they carry a small spray bottle for spritzing their face to cool down.
The Bandana also comes in handy to cover your nose and mouth in case you encounter winds and blowing sand.
A hat is really necessary in desert conditions. The conditions most of your trek will be in. While any type hat is better than nothing, the type that covers your ears with shade, in addition to shade for the top of your head, is highly recommended. During summer the type you can water soak adds a great cooling effect.
Sunglasses are a must. Protect your eyes from the glaring sun. They also come in handy during winds and blowing sand.
Sunscreen goes without saying in this climate.