Does eating ice burn calories

The heat of fusion (change of state from liquid to solid) of water is 80 cal/g. That occurs in atmospheric conditions at zero degrees Celsius. The body regulates it's temperature to be 37 degrees C (98.6 deg F). The sensible heat gain of the water then is an additional 37 cal/gram. The body's metabolism has to heat that water from ice to body temperature, 117 cal/gram of ice. Of course, there are 1000 physical calories per 1 dietary Calorie. Doing the math and simplifying the numbers a little, the water consumed as ice will gain 100 Calories/liter. Where does that heat come from if it isn't additional metabolic energy over and above the body's normal metabolism? Just be careful on the rate of consumption to avoid the painful ice cream head ache or the stomach ache caused by consuming too much cold. Chewing ice is not good for the teeth, so just drink crushed ice with just enough water to make the solution flow. Enjoy a smoothie, a slurpee or slush that is plain ice with no sugar. Flavor it with lemon or lime similar to what you do with a glass of water. Make the slushie with low calorie flavored water. In order to get the benefit of 68% of the energy, your beverage must be consumed as ice. If it is liquid water, that energy was absorbed by the room air. But, it seems that 2 liters daily would burn 200 calories.