Every activity results in a certain amount of calories burned, regardless of how active or inactive a person is. Sleep certainly qualifies as an activity, so the unsurprising answer to the question "Are calories burned during sleep?" is "Yes." The number of calories burned varies from person to person. The average person burns about 77 calories an hour while sleeping, but the actual number of calories burned by a specific individual depends on his or her Basal Metabolic Rate.
Basal Metabolic Rate
The Basal Metabolic Rate (BMR) is the minimum rate at which your body burns calories when at rest. The calories are burned in order to support the body's autonomic systems: breathing, heart rate, nervous system and body temperature. The BMR is primarily influenced by the interaction of the environment with a person's genetics. Tall, thin people tend to have a higher Basal Metabolic Rate than the shorter and rounder, and women typically have a lower BMR than men. The older you get, the lower the BMR. Caloric restriction tends to lower the Basal Metabolic Rate, so as you sleep, it will fall as well. One reason eating breakfast is critical to almost every diet is that without that meal, your BMR will stay low, and fewer calories will be burned than if you had eaten breakfast.
Sickness raises the BMR, as does prolonged exposure to temperature extremes. Sleeping in a cold room will help, but it's not a good idea to start hanging around the infected in the hopes that becoming ill will help you lose weight. Bed rest means lost muscle mass, and all other things being equal, a muscle at rest burns more calories than the equivalent amount of fat at rest. Strength training is an excellent way to increase your BMR. Frequent periods of exercise spread across an entire day will also raise not only the Basal Metabolic Rate, but your overall metabolism as well, leading to more calories being burned during every activity, including sleep.