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The mechanisms by which heat is delivered to Antarctic ice shelves are a major source of uncertainty when assessing the response of the Antarctic ice sheet to climate change. Direct observations of the ice shelf-ocean interaction are extremely scarce and in many regions melt rates from ice shelf-ocean models are not constrained by measurements. Our two years of data (2010 and 2011) from three oceanic moorings below the Fimbul Ice Shelf in the Eastern Weddell Sea show cold cavity waters, with average temperatures of less than 0.1°C above the surface freezing point. This suggests low basal melt rates, consistent with remote sensing-based, steady-state mass balance estimates for this sector of the Antarctic coast. Oceanic heat for basal melting is found to be supplied by two sources of warm water entering below the ice: (i) eddy-like bursts of Modified Warm Deep Water that access the cavity at depth for eight months of the record; and (ii) fresh surface water that flushes parts of the ice base with temperatures above freezing during late summer and fall. This interplay of processes implies that basal melting at the Fimbul Ice Shelf cannot simply be parameterized by coastal deep ocean temperatures, but instead appears directly linked to both solar forcing at the surface as well as to the dynamics of the coastal current system.