Question

the temperature does not rise during the process of melting and boiling, though heat energy is constantly supplied?

Answer 1

HERE IS YOUR ANSWER DEAR FRIEND!!!!!
The temperature doesn't rise during the melting and boiling, though heat is produced because the extra amount of heat is used up to break up the molecular bonding during the process of Boiling and evaporation.
In simple, this is known as the latent heat of Vaporisation.
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Answer 2

$\large\boxed{\fcolorbox{blue}{yellow} {Answer}}$

Once water starts boiling, all the heat supplied to it is used in conversion of water into steam at the boiling point of water.

Hence, there is no rise in its temperature.

$\large\boxed{\fcolorbox{blue}{yellow} {Additional Information }}$

★ Boiling point of liquid :

The constant temperature at which a liquid transforms into gaseous state is called the boiling point of the liquid.

★ Latent heat of fusion :

The amount of heat energy absorbed at constant temperature by unit mass of a solid to convert into liquid phase is called the specific latent heat of fusion.

★ Latent heat of vaporization :

The amount of heat energy absorbed at constant temperature by unit mass of a liquid to convert into gaseous phase is called the specific latent heat of vaporization.

Hope it helps!