The temperature of water does not change during melting. This is because the energy supplied to the ice is used to overcome the latent heat of fusion, which is the energy required to change a substance from a solid to a liquid at its melting point. This energy goes into breaking the bonds between the water molecules in the ice, and does not result in an increase in the temperature of the water.
Once all of the ice has melted, the additional energy supplied will then begin to raise the temperature of the water.