Hello Biologyfool,

Respectfully disagree. The absorbed energy is unseen, increased atomic vibration.  Only when the ice has absorbed the required total energy is when it melts. Unmelted ice has a thermal conductivity coefficient too, as linked here:

http://tinyurl.com/lkwrg

The colder the ice: the faster it absorbs heat.  It is all very complex, way above my limited understanding.  Ongoing research is trying to get a better handle on this:

http://www.usap.gov/scienceSupport/sciencePlanningSummaries/2003_2004/indiv_projs/O253.htm

I assume supercomputer modeling is required to adjust for all the inter-related physical effects of solar radiation, albedo reflectivity, air & water thermal currents, snow insulation, glacial flow rates, etc.... on & on & on.

Bob Shaw in Phx,AZ  Are Humans Smarter than Yeast?

You are talking about heat of fusion. For example if you place a pot full of ice on the stove and turn it on high a constant amount of energy is being applied. The ice begins to melt but the water stays at zero, once all the ice has melted then the water temp climbs.  The energy is absorbed when the melting occurs. Now the bad part is all earths ice reflect a great deal of energy beacause it is white. How much more will we retain after our reflective blanket is gone?