When ice is heated the surroundings have room temperature. the ice being cooler absorbs the heat provided and the temperature of the surroundings is not affected. when the ice is converted to water and is then heated, the water as well as the surroundings absorb the heat as they both have the same temperature.
When ice at -10°c is slowly heated its temperature increases because it absorb some energy .when ice melt its temperature is constant because its specific heat constant is infinite hence from equation Q/(mc) = t ; t = 0 hence temperature not increases.
when whole ice is melt , on further heating its temperature increases because it has finite specific heat constant.