A calorie is the amount of energy required to raise 1 milliliter of water 1 degree Celsius.
A food calorie is really 1000 calories, or a kilocalorie.
Therefore a food calorie is the amount of energy required to raise 1 liter of water 1 degree Celsius.
Body temperature is 37C (98.6F)
If you drink cold beer, your body must expend energy to raise the beer from its temperature at intake to body temperature.
For example, just to make the math simple, let’s say you drink half a liter of beer (about a pint) which you pulled out of the 4C refrigerator, you would burn 0.5 food calories per degree, or about 16.5 food calories:
Starting temp: 4C Ending temp: 37C Delta: 37-4 = 33C Volume: 0.5L Energy: 33 * 0.5 = 16.5 kcal
Given that your average American lager beer has about 12 (food) calories per ounce, we can extrapolate by volume, and then calculate net savings for a range of temperatures.