Question

why does the temperature remain constant during melting of ice even though the heat is applied constantly?​

Answer 1

Because latent heat of fusion is provided to ice in this case. Latent heat of fusion is the process in which solid is converted to liquid. Here the energy provided was just used to convert the ice into water.

Answer 2

The temperature remains constant during the change of state of a solid to liquid, because the eneegy which is actually supplied to change the state is used up in breaking down the force of attraction between the particles of solid.

$\textbf{Then when temperature will rise of heat is supplied continuously ? }$

Tempertaure will only increase when the whole solid get melted to form liquid, then the heat supplied will start to break the force of attraction between the particles of liquid.