What happens to ice when energy is supplied at a constant rate in terms of the changes in energy of the molecules?

If we start with water at 263K (ice) then the molecules are positioned in a regular lattice structure held in place by hydrogen bonds. The molecules have some vibrational energy but not much translational energy (kinetic energy). As energy is supplied the molecules gain kinetic energy and this corresponds to an increase in temperature because temperature is directly proportional to internal energy change. The water reaches 273K where the energy now begins to go into the bonds between the molecules and so in this transition phase the temperature is constant. This energy is called the latent heat of formation. In this transition the potential energy changes not the kinetic energy.

Now we have liquid water where the molecules have significantly more kinetic energy as they are not held in place with intermolecular bonds. Therefore, there is less potential energy as there are weaker bonds. A similar process will occur when the water gains even more energy and it reaches 373K and forms a gas which has the most kinetic energy and the least potential energy.