During the day the cloud cover blocks the sunlight which helps keeps us a bit cooler but during the night it does the opposite. The clouds act like a blanket and trap the heat down to the earth’s surface.
The earth hits peak radiation cooling during a clear sky, calm wind, and a dry night. The drier the air mass the lower the humidity. Low humidity areas like desserts and high elevation can generate a large temperatures drop. The lack of clouds allows the earth to radiate its heat freely and quickly. Having clouds overhead will trap some of the radiated heat back down to the earth’s surface and not allowing it to escape into space. This is the same reason why we use blankets to keep us warm. The thicker the blanket the warmer you will be.