Not only is heat required to raise the temperature of the solid to the melting point, but the melting itself requires heat; see also latent heat and heat of fusion.

From a thermodynamics point of view, at the melting point the change in Gibbs free energy (G) of the Material is zero, because the enthalpy (H) and the entropy (S) of the material are increasing (H,S > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that:

http://upload.wikimedia.org/math/0/9/a/09aba87f1f9c817fa0b4f838a9478fdc.png

The “T”,“S”, and “H” in the above are respectively the temperature at the melting point, change of entropy of melting, and the change of enthalpy of melting.

Freezing, the process of turning a liquid to a solid, is the opposite of melting. The melting point and freezing point are usually the same temperature. See the phase article for more detail.