I used to live in Tucson, AZ., so I can back up falcon's remarks about southern Arizona (and clarify waltz's). That is indeed the Sonoran Desert. Tucson itself is in a valley which is basically "low desert" in its flora (dominated by mesquite and sagebrush) and fauna. But in the rocky foothills of the mountains and of the hills going east on I-10, one encounters "high desert" -- characterized by a different flora especially (such as the famous saguaro cactus).

In that area high desert, or even Tucson's relatively low valley (I don't think Tucson is at or over 5,000 feet), is only marginally cooler than the low desert characteristic of the valley of Phoenix. When Tucson is at 105, Phoenix is typically at 115. Hila Bend, usually the hottest place in Arizona, tops even that, as can the very low Yuma. (I passed through Yuma one noon hour when it was 120 degrees and relatively humid. "How can you live in a place like this?" I asked a local. "Air conditioning," she replied.)

Tucson does have more seasonal variation than Phoenix does. It can actually snow once in a while in the valley itself, as it normally does in the mountains.

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