Yes, DA, it won't happen tomorrow; but I intended the question to be hypothetical and to serve soley as a basis for discussing a key point: the temperature gradient.

I'll simplify the question, and reverse it, to avoid confusion:

Would it still require 4.1855 joules (1 calorie) to raise the temperature of 1g of water (ice) from, say, 1.7K to 2.7K, or is the physics different at close to absolute zero?

"Time is what prevents everything from happening at once" - John Wheeler