A large hiking partner who can cast shade on you! Seriously, my survival gear has been outlined in a few other posts so I won't rehash it here but there are some specialized items that I bring when hiking in the desert.
1) Gookinaid or a similar sodium-replacement powder to help replenish electrolytes and prevent hyponatremia. I also bring salty pretzels or nuts which are good for snacking on during the day.
2) Brimmed hat. I've used Tilley Hats for years as they hold up to UV rays, are lightweight, and can take a beating. Lately, I have been using cowboy style hats as they have a wider brim and protect my head better. Some desert hikers I know use umbrellas while on the trail. I don't but have one in my truck in case I break down and have to hike out (or stand over my buddy while he changes the tire).
3) Sunscreen. This sounds like a no-brainer, but I am amazed at how many hikers get severe sunburn at the Grand Canyon just venturing out unprotected for a few hours. I use SPF 30 and always have a small bottle in my pack and truck. Quality sunglasses also accompany me.
4) Lightweight cotton shirt. This is a long-sleeved button up shirt made of quick-dry cotton. Columbia and REI both make their own versions of these. In most environments, cotton is the absolute worst fabric to wear in the outdoors as it fails to insulate when wet and will rob your body heat from you 240 times faster than if you were naked! But in the desert, that cooling ability can work to your advantage. So, for the hotter months, I do wear a cotton shirt but also pack along another shirt.
5) Down jacket and wool hat. No kidding on this one. The desert is a land of extremes and you have to prepared not only for heat-related injuries like dehydration but also hypothermia. The record temperature in my home state of Arizona occurred in Yuma where it went from 120 degrees during the day to 39 degrees at night!
6) Extra water. This can't be overstated. Too many dayhikers have perished from heat stroke in the Southwest because they didn't plan ahead. In my pack, I will have 2-6 quarts of water when hiking long-distance in the heat. Two gallons per person per day is what I recommend carrying in your vehicle. This is in addition to the water for your hike. It's called a desert for a reasonbecause there is no waterso don't plan on that spring on the map being there. The most reliable source of water comes from your kitchen tap. Carry Plenty!!
If you want to read an eye-opening account of life in the desert, check out Death in the Grand Canyon by Tom Myers. It provides insightful lessons of what to do and not do when hiking in the "Land of Little Water."