Is it true that the temperature of a substance remains constant during its melting point or boiling point?

The above statement is true.

This is because the heat given is continuously used up in altering the state of the substance by overcoming the forces of attraction between the particles, the temperature of a substance remains constant at its melting and boiling points until the entire substance melts or boils. Latent heat of fusion/latent heat of vaporisation refers to heat energy absorbed without causing a temperature increase. Hence, the temperature of a substance remains constant during its melting point or boiling point.