Paraphrase

(Acutal)On our recent Arctic expedition named AGAVE to the Gakkel Ridge (~85N) in 2007 we found evidence of recent explosive volcanic eruptions. However, most of the heat flow at the Gakkel Ridge seems to be diffusive and slowly seeping out. In any case, heat releases from the Arctic sea floor do not get higher up in the water column than, typically, ~500-1000 m from the ocean floor due to constantly mixing with ambient water on its way up (so-called entrainment). None of these will have any impact on the Arctic sea ice as the heat is trapped in the deep ocean and is unable to communicate with the upper ocean and sea ice.

http://dotearth.blogs.nytimes.com/2008/07/01/whats-up-with-volcanoes-under-arctic-sea-ice/

(Paraphrase) Even though these active volcanoes have been erupting under the Arctic ice they are located so deep that the heat never really reaches the ice. In fact, the heat normally only gets up to 500-1000 meters above the ocean floor leaving the ice that sits 4000 meters above the floor untouched.