Probably the fault is in your water heater. There is nothing of such sort that the water gets heated more at the lower temperature. I would like to talk a bit scientifically here:
When you heat the ice then, initially the heat goes to provide latent heat of fusion of ice. When that latent heat is provided then the ice melts. At present the temperature of both ice and melted ice remain zero. When whole ice has melted and the heating goes on then all the heat goes onto to increase the temperature. When the temperature goes till 100 degree celcius then the heat goes to provide the latent heat of vapourization. Here both the steam and water has same temperature that is 100 degree celcius. All the process above is at 1 atmosphere pressure. If you increase or decrease the pressure then it is all different.