Question

Why does the temperature remain unchanged until the entire solid changes into liquid even if

we are heating the solid?

Answer 1

During the change of state , when a substance absorbs or gives heat, there is no change in average kinetic energy of its molecules and so the temperature of the substance does not change during the change of state.

Answer 2

This happens because the latent heat of fusion or melting gets hidden on the surface of the solid. This latent heat is equivalent to the latent heat of fusion.
This also results in an unchanged temperature even though the solid melts into its liquid state.