Question

Temperature remains constant until the whole of the solid changes to liquid though the heat energy supplied continuously? Why?

Answer 1

because the temperature is absorbed to overcome the forces of attraction between the particles and is known as latent heat.
hope it helps

Answer 2

This is known as the Latent heat of fusion:
The Latent Heat of fusion is the amount of thermal energy required to cause a a liquid to freeze (by taking that much heat out) or a solid to melt (by putting that much heat in).