Have lived and bicycled in the desert since 1978. "Warmest" I commuted in: 117 degrees with 2% humidity. Do-able? Yes. Fun? No!
In summer ride early A.M. and before mid-day; wear light colored non-nylon jerseys/clothing. Wear a cycling cap (good for shading eyes, keep noggin cool, use as emergency rag). Wet the hat before you leave; oh it will dry in 20 minutes, but makes for a cool start. Re-wet as necessary. Carry cold water. How? Freeze a couple bottles the night before, about 3/4 full then add water before you step out. Sunscreen? You bet!
Wet a bandana and wrap it around the neck; again it will dry but sure keeps the body temp down a couple notches. Re-wet as needed.
Once it is over 100 degrees do not overinflate tires: maybe drop pressure about 10% as road surface can be 140+ degrees.
Do take a break every so often . . . even if you have to stand in the shade of a telephone pole or saguaro!
Watch your potasium (bananas!) and salt (pretzels, chips) intake too. Avoid alcohol and caffinated drinks (diuretics).
Have toured from the Grand Canyon to Mexico on a tandem 4 times and once on my racing single in late September. Temps vary from hi-20s at Lake Mary to 100+ around Globe and Tucson.
Yes touring is do-able in the desert, with precautions and preparation.

Pedal on TWOgether!
Rudy and Kay/zonatandem