The poleward flow of the Leeuwin Current dominates the surface circulation off Western Australia. Along its path, it cools by about 5¿C over 1350 km. Based on an eddy permitting simulation using the Parallel Ocean Program model, we find that 70% of the heat advected into the coastal region off Western Australia by the narrow mean jet is transferred to the ocean interior through eddy heat fluxes. The eddy fluxes are associated with processes operating at submonthly timescales and despite the current's clear seasonal variability, seasonal rectification plays little role in the mean heat balance. The 43 TW transferred offshore by eddies is the primary means by which the ocean interior (22¿S--34¿S and east of 107¿E) is warmed and the Leeuwin Current cooled. The Leeuwin Current jet and the eddies allow air--sea fluxes to transfer over 40 W m-2 of heat to the atmosphere in the southeast Indian Ocean.