Subglacial hydrologic systems regulate ice sheet flow, causing acceleration or deceleration, depending on hydraulic efficiency and the rate at which surface meltwater is delivered to the bed. Because these systems are rarely observed, ice sheet basal drainage represents a poorly integrated and uncertain component of models used to predict sea level changes. Here, we report radar-derived basal melt rates and unexpectedly warm subglacial conditions beneath a large Greenlandic outlet glacier. The basal melt rates averaged 14 mm ⋅d-1 over 4 months, peaking at 57 mm ⋅d-1 when basal water temperature reached +0.88 ∘C in a nearby borehole. We attribute both observations to the conversion of potential energy of surface water to heat in the basal drainage system, which peaked during a period of rainfall and intense surface melting. Our findings reveal limitations in the theory of channel formation, and we show that viscous dissipation far surpasses other basal heat sources, even in a distributed, high-pressure system.