The hottest temperature on record in a desert (and the entire world!) was 134 degrees Fahrenheit (56.7 degrees Celsius). It was recorded in Death Valley, California on July 10, 1913. That's only about 5.5 hours from here! (University of California Santa Barbara).

The hottest temperature ever recorded in a desert was actually recorded right here in California’s own Death Valley in 1913. The Mojave Desert in Death Valley reached 134° F. That’s scorching hot!

A quick Google search comes up with a number of about 58 degrees C (136 degrees F) in northern Africa. I don't know who collected these data, though.