How much heat has gone into melting the Arctic Ice?

The climate change contrarians are making much of the fact that the upward trend in global surface temperatures has slowed or stopped since 1997.

Climatologists point out that 98% of heat applied to our planet goes into the sea, and the heating of the sea continues unabated. Unfortunately, this fact is just too difficult for most journalists to pass on.

I am interested in one aspect of where the heat goes, namely, the melting of Arctic Ice. Every skuledboy kno that the Arctic ice is melting.  If we apply gentle heat to a beaker of water containing a lump of ice, the water temperature will not increase until the ice has finished melting.

This shows the rate of melting, which has picked up over the period that the contrarians are so excited about.

So how much ice has melted?This figure shows the volume variation: (as ever, click on the image to enlarge it)

http://psc.apl.washington.edu/wordpress/research/projects/arctic-sea-ice-volume-anomaly/

The September mean volume for 1979-2012 stands at 12,000 cubic km of ice.
The September value for 2012 stands at 3,000 cubic km of ice.
Therefore we have lost 8,000 cubic km of ice, since about 1997 (see this figure).

1 cubic kilometer of ice = 10 to power 15 grammes of ice

Now 80 calories of heat are required to melt 1 gramme of ice.

Therefore to melt 1 cubic km of ice we need 8 * 10 to power 16 (10^16) calories
To melt 8000 cubic km ice we need 6.4 * 10^20 calories

That is 2.7 * 10^21 Joules.
That is 2,700,000,000,000,000,000,000 Joules.

That is as far as I can take it at present. In the last 16 years, 10^21 joules have gone into melting the Arctic ice since 1997.

This is clearly a lot of heat, but I have no idea how significant it is compared to the earth's energy budget.

It is 2*10^8 Hiroshima bombs, (200,000,000) spread over 15 years, but how much surface warming would it represent, if, instead of going into melting ice, it went directly into heating the surface air?