Question

Suppose we have an ice cube on the counter of a warm room. We expect to see the ice cube melt and the room to cool off a little. But is it possible that the ice cube might get colder with the room heating up (energy transferring from the ice cube to the room by heat)?

Answer 1

No.

At least, not spontaneously. The Zeroth Law of Thermodynamics essentially states that heat will spontaneously move from hotter to colder bodies, so the net effect of ice sitting in a warmer room will be heat transfer from the room to the ice.

Temperature is a measure of the average kinetic energy of particles in a sample. Heat transfer occurs because fast-moving particles from a "hotter" sample collide with slow-moving particles from a "colder" sample, and transfer some of their kinetic energy to these colder particles. The colder particles therefore gain kinetic energy, so their temperature increases, while the hotter particles lose kinetic energy, so their temperature decreases.