Cloudy nights are warmer than clear nights because of

Cloudy nights are warmer than clear nights primarily due to the interaction of clouds with terrestrial radiation. During the day, the Earth absorbs shortwave solar radiation (insolation) and, at night, it re-emits this energy back into space as longwave infrared radiation, also known as terrestrial radiation [5]. While the atmosphere is mostly transparent to incoming shortwave radiation, clouds act as a physical barrier to outgoing longwave radiation [3]. Clouds absorb this terrestrial heat and re-emit it back toward the Earth's surface, effectively trapping heat within the lower atmosphere [4]. This process is often compared to a blanket or a greenhouse effect, where clouds close the 'atmospheric window' that would otherwise allow heat to escape into space. Consequently, the presence of clouds prevents the rapid cooling of the surface that occurs on clear nights [4].

Sources

1. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 21: Horizontal Distribution of Temperature > Insolation > p. 282
2. [5] https://en.wikipedia.org/wiki/Outgoing_longwave_radiation
3. [3] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 22: Vertical Distribution of Temperature > 22.2. Lapse Rate > p. 295
4. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 24: Hydrological Cycle (Water Cycle) > Explanation: > p. 331
5. [4] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 21: Horizontal Distribution of Temperature > 21.5. Heat Budget > p. 293