Can I lower the effective calories of a drink by cooling it?

If a calorie is defined as the energy required to heat 1ml of water by 1 degree Celsius. If I refrigerate a drink to 4c in a fridge and drink it, my body needs to burn more energy to maintain temperature and thus burns more energy in proportion to the volume and temperature of the colder fluid consumed.

So if I drink a cold drink vs a warm drink, am I effectively minimizing calories?

Ex. 1cup (250 ML) @ 4c requires 8,250 calories to be heated to body temperature of 37c

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EDIT: I now know my logic was sound, but since I was confusing Calories with calories, my math was off by 10^(3). thanks everyone!