A desert, according to "National Geographic," (see Reference 1) is an extreme case of a "dryland," a place that "lose[s] more moisture through evaporation than [it] receive[s] from annual precipitation." With little moisture in the soil, there's even less in the air to moderate extremes of temperature.
During the day, the sun pours down "shortwave" radiation -- visible light. The soil, even in a desert, reflects back mostly "longwave" radiation -- heat that is not visible to human beings. Longwave radiation continues to rise even when shortwave radiation stops at sunset.
As defined in the American Meteorological Society's "Glossary of Meterology," when an area of the Earth's surface radiates more longwave energy up than some source in the atmosphere, such as the sun, sends down in shortwave form, the energy deficit at the surface results in radiational cooling. (See Reference 3.)
