I am afraid you cannot find the answer from pure energy balance.
The answer will depend on the rates of heat transfer from the water to the ice and steel to the ice.
There will be a temperature gradient building up around the ice block.
During melting you have a non-equilibrium situation. Water, ice and steel have different temperatures. I understand that you want to know what will be the temperature of the steel (assuming it is uniform, which may be a good approximation for a good conductor) at the very moment when the ice is completely melted.
So the answer will depend on the specific rates of heat transfer.
Unless you want to wait until equilibrium is reached again and then everything will be pretty much 12 degrees.