Hey Samwik

your right about heat transfering into the water as the ice melts.
nice point and a little more info , 1 cu meter of water
can store 334 MJ / 317,000 BTU's / 93,000 Wh's
of energy.
Quote:
Thermal energy storage is made practical by the large heat of fusion of water. One metric ton of water, just one cubic meter, can store 334 MJ (317 k BTUs, 93kWh or 26.4 ton-hours). In fact, ice was originally transported from mountains to cities for use as a coolant, and the original definition of a "ton" of cooling capacity (heat flow) was the heat to melt one ton of ice every 24 hours. This is the heat flow one would expect in a 3,000-square-foot (280 m2) house in Boston in the summer.


http://en.wikipedia.org/wiki/Thermal_energy_storage

3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.