“fat cells burn around 2.05 Calories per pound, so you’d gain a lot of weight” in order for for the extra fan to burn off the extra calories you’re eating.

Sad reality.

Fat substitutes may actually lead to weight gain

the body may, when anticipating fatty or sweet foods, get primed for a big dose of calories. When those calories aren’t delivered, the body feels cheated and compensates by overeating, trying to achieve the sensation it expected to get from eating the delicious, high-calorie food it expected in the first place.

People ate an average of nearly 300 calories more when they were sleep-deprived compared to when they were well rested, research presented at an American Heart Association revealed. And the calories overwhelmingly came from junk foods like ice cream and fast food.

In one study, researchers found that people who received only four hours of sleep a night for two nights experienced:

18 percent reduction in leptin
28 percent increase in ghrelin

Effects of Insufficient Sleep

It’s interesting to see some degree of quantification here.