Thermodynamically speaking, the difference between solid and liquid water at 0 degree is the amount of energy in the system. if energy is added to ice its not used to increase the temperature but goes into the melting process which, in itself consumes energy as the disorder (or entropy) of the system increases. Its similar to the phase equilibrium of the water/vapour system. Evaporation consumes energy, condensation gives off energy, but both happens at the same temperature (not necessarily 100�C, though)