The biggest solar thermal plant ever built is in the Mojave Desert of California and generates 80 megawatts. (The biggest single photovoltaic installation produces 12 megawatts.) Solar thermal power prices range from 11 cents to 15 cents per kilowatt-hour, making it more expensive than natural gas generation at its lowest price, around 7 cents, but less expensive during peak hours.
Aside from the sweltering daytime heat and the freezing night-time temperatures, the biggest problem for folks living in desert regions is finding sources of water.