Clouds act as a blanket, trapping heat from the earth and preventing it from escaping into the atmosphere. This is why it is often warmer on cloudy nights than on clear nights.

Also, when the sky is clear, the air is more humid. This is because the water vapor that condenses to form clouds during the day evaporates at night when the air is cooler. The more humid air is, the more it can hold heat.

Therefore, a clear night sky would cause the temperature to drop more than a cloudy night sky.