Significance Subglacial drainage systems control ice sheet flow and the quantity of ice discharged into the ocean. However, these systems are currently poorly characterized, from a lack of direct observations. This shortcoming is problematic, as changes in drainage systems can result in a markedly differently ice sheet response. Here, we present a radar-derived record of basal melt rates with colocated borehole observations, showing unexpectedly warm subglacial conditions beneath a large outlet glacier in West Greenland. The record is unprecedented because the observed basal melt rates are several orders of magnitude higher than predictions and previous estimates. Our observations show that the effect of viscous dissipation from surface meltwater input is by far the largest heat source beneath the Greenland Ice Sheet.