Look a little closer
Deserts are famous for daytime heat, yet many cool sharply after sunset. Sand does not manufacture cold; clear dry air and a moisture-poor surface simply retain daytime energy poorly.
Few clouds allow strong sunlight to heat the ground by day. With little water available, less incoming energy is spent on evaporation, so the surface and shallow air above it warm quickly.
After sunset, the ground emits energy upward as infrared radiation. Clouds act like a blanket by absorbing some of that radiation and emitting part back downward. Under a clear desert sky, this effect is weak.
Water vapor also absorbs and emits infrared energy. Dry air contains less of it, allowing surface heat to escape more effectively. Sparse vegetation and dry soil provide little moisture to moderate the swing.
Not every desert night is freezing. Season, elevation, latitude, wind, cloud and humidity create large differences. Coastal deserts or nights with incoming moisture may have much smaller temperature changes.
The useful generalization is not that deserts always have cold nights, but that they favor a large day-night range. Little blocks sunlight during the day, and little returns outgoing infrared energy at night, so surface temperature can change rapidly.
