For day hikes, I go for a cotton, long-sleeve, collared dress shirt - typically one I have retired from office wear. Or $4 at Goodwill. It keeps the sun off and you know how "Cotton doesn't keep you warm when wet"? - that's a good thing in the desert. I much prefer to apply water to my shirt, bandana and hat from water sources or even from my water bottle than to sweat out the same water. My clothes aren't so salty, I didn't have to treat so much water, and especially if I'm crossing streams, it's quick and easy.
On overnight trips, I still might bring that cotton shirt, but I'd change out of it as the sun sets and go towards synthetic layers and/or a puffy to keep warm. I've got a loose fitting, LS, collared nylon shirt that feels good (air blown into the fibers?) and not clammy. Ex Officio, I think.
A baseball-style cap and a cotton bandana is one of the most compact, lightweight hat options but it doesn't allow as much breeze around your face and neck as a broad-brimmed hat. I'm Celtic and I just accept that I need to wear stupid-looking hats. I haven't tried them on a hike, but I note that Mexican gardeners and my geologist co-workers in SoCal wear those huge straw hats that shade you all around. $6 at the garden store. Get one with or add a chin strap string for the wind.
I've liked using my Chrome Dome silvered umbrella. It feels about 15F cooler under it. I use it more at high elevation where the UV is more intense, but portable shade is great in the low desert, too. I can position it hands-free through a backpack sternum strap and an epaulet on my shirt's shoulder. Don't forget that you can position it on a thinly-leafed desert shrub to create solid shade underneath during a nap or lunch. Your tarp or rainfly can do that as well, but only when you're stopped.
START SLOW if you're not from a hot climate. Your body will take 1-3 days to adjust to sweating so much more. I've been hurting on a few trips to New England in the humid summer or the tropic when escaping an Alaskan winter. If I do 2 days of low-intensity or town-based activities without spending all my time in air conditioned cars and buildings, I do better once I hit the trail. Coming from the NE, I'd say expose yourself to the heat of the day at home prior to your trip. You may find the "dry heat" easy in the comparison.