Tell Me About Growing Potatoes
Potatoes are little more difficult to grow in the desert; they prefer acidic soils and cool temperatures. If you have a rich soil, try planting the "eyes" toward the end of July or even August and let the monsoon help you get your crop going. If you can make it through September, the fall should cool it down and you might harvest a nice crop for Thanksgiving.
Here's the page in the Master Gardeners manual: http://ag.arizona.edu/pubs/garden/mg/vegetable/potatoes.html