The "specific heat capacity"? Not the "heat of melting"?
The "specific heat capacity" of anything is defined as the amount of heat necessary to raise its temperature one degree celsius (which would also be one degree Kelvin). Freeze a large amount of ice, well below 0 celsius (and that's HARD precisely because the specific heat of ice is very high). Pour a comparatively small amount of hot water (just below 100 celsius would be best) over the ice. After it has come to equilibrium, measure the temperature of the ice. Since you know (I am assuming) the specific heat of water and its original temperature, you know how much heat was transferred to the ice and so know how much heat it took to raise the ice by whatever temperature change you found.
That's simplest conceptually but the temperature change might be hard to measure. The point of using "comparatively little water" is that you can ignore the water changing to ice.
To be more precise, you might do it this way: freeze a measured amount of ice, again well below freezing (the more increase in temperature before it melts the more accurate your result) and record its temperature. Pour a large measured amount of water at a measured temperature. Assuming that all the ice melts: measure the temperature of the resulting water. If you know the specific capacity of water, you can calculate how much heat the water gave up in going from its original temperature to the final temperature. If you know the "heat of melting" of ice, you can calculate how much of that heat was used to melt the ice- deduct that from the heat you got from the water. Also calculate the heat necessary to raise that melt water to the final temperature and deduct that from the remaining heat. The heat left is the heat that was used to raise the temperature of the ice from its initial value to 0. The specific heat capacity of ice is that heat divided by the change in temperature.
It will be large, ice is a very good insulator.
