Why is there no change in the temperature when the process of melting takes place?

Since the energy that goes into performing the phase change goes into breaking intermolecular forces, the temperature of the molecules does not change.

Explanation:

During a change in state the heat energy is used to change the intermolecular interactions between the molecules. In the case of melting, added energy is used to break the interactions between the molecules. In the case of freezing, energy is lost as the molecules bond to one another. These energy exchanges are based mostly on loosening the vibrational motions. They are changes in interaction energy between the molecules.