Temperatures drop steeply in deserts at night because the dry air does not hold down the energy absorbed by the soil during the day as light and radiated back as heat, creating an energy deficit and causing "radiational cooling."
Dry Heat, Dry Cold
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.
Bright Shortwave, Dark Longwave
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 short wave radiation stops at sunset.
Imbalance of Power
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 short wave form, the energy deficit at the surface results in radiational cooling. (See Reference 3.)