Basal hydrology of the Greenland Ice Sheet (GIS) influences its dynamics and mass balance through basal lubrication and ice–bed decoupling or efficient water removal and ice–bed coupling. Variations in subglacial water pressure through the seasonal evolution of the subglacial hydrological system help control ice velocity. Near the ice sheet margin, large basal conduits are melted by the viscous heat dissipation (VHD) from surface runoff routed to the bed. These conduits may lead to efficient drainage systems that lower subglacial water pressure, increase basal effective stress, and reduce ice velocity. In this study we quantify the energy available for VHD historically at present and under future climate scenarios. At present, 345 km³ of annual runoff delivers 66 GW to the base of the ice sheet per year. These values are already ∼ 50 % more than the historical 1960–1999 value of 46 GW. By 2100 under IPCC AR5 RCP8.5 (RCP4.5) scenarios, 1278 (524) km³ of runoff may deliver 310 (110) GW to the ice sheet base. Hence, the ice sheet may experience a 5-to-7-fold increase in VHD in the near future which will enhance opening of subglacial conduits near the margin and will warm basal ice in the interior. The other significant basal heat source is geothermal heat flux (GHF), which has an estimated value of 36 GW within the present-day VHD area. With increasing surface meltwater penetration to the bed the basal heat budget in the active basal hydrology zone of the GIS will be increasingly dominated by VHD and relatively less sensitive to GHF, which may result in spatial changes in the ice flow field and in its seasonal variability.