Many things play a role in how cold the temperature gets at night. Here are the ones that come to mind immediately:
Clouds, like so many other parts of the weather, can be a mixed blessing. During days like Monday, they serve to hold the temperature down by blocking the sun and providing the cold rain. In a similar way, they can provide the opposite effect at night. By covering the earth, clouds help warm the air close to the ground by emitting infrared radiation in all directions, including towards the surface of the earth.
On a clear night, the dew point helps to determine the low temperature. With few to no clouds in the sky, the warm air escapes and the temperature can drop quickly. However, it’s unlikely that the temp will drop below the dew point. Once the temperature reaches the dew point, fog or frost may form, depending on the amount of moisture in the air and the time of year.
Wind also plays a role in how cool the overnight low will be. A breeze would serve to mix the warmer air aloft down to the surface. On a night when winds are calm, the temperature can drop quickly.
Elevation also makes a difference. Warm air rises, and cold air sinks. So, lower lying areas tend to collect cooler air than higher terrain.
One last thing that can affect the temperature at night is ground cover. In the winter, the low will be colder if there is snow on the ground. In the city in the summer, the blacktop and concrete surfaces that heat so quickly during the day release heat very slowly at night – keeping the city a bit warmer than the country. This phenomenon is called the urban heat island effect.