The temperature of any substance remain constant during the change of state because the heat energy supplied is used up in changing the state of matter and also this heat is used for breaking of several bonds or attractive forces.This heat, which does not raise the temperature of the body, is called Laten heat.
Or
Temperature of any substance remains constant because the heat supplied to increase the temperature is utilised in changing the state of matter. this is because of latent heat.
Or
Since the heat is used to overcome the force of attraction, the temperature of the substance does not change. The heat energy absorbed in this case is called as the latent heat. The temperature of the substance remains equal to the latent heat provided to or released by it. That's why for any substance, the temperature remain constant during the change of state.