The thermal state at the bed of a large ice sheet is a critical boundary condition governing its future evolution. Radar surveys provide an opportunity for direct but remote observation of the ice-sheet bed, and therefore offer a means of constraining numerical ice-sheet models at the ice–bed interface. Here we have processed results of radar surveys of the Greenland Ice Sheet undertaken by the Program for Arctic Regional Climate Assessment (PARCA) between 1999 and 2003, to explore this opportunity. We consider the robustness of the measurements in the context of uncertain dielectric losses in the ice sheet, concluding that the observed radar signal characteristics reflect the character of the bed itself rather than that of uncertain englacial absorption. However, the identification of thaw is restricted to areas where subglacial water has sufficient depth to influence the radar reflection. We derive a map of inferred areas of subglacial thaw, and compare our results with other studies predicting regions with temperate bed. We show that in many areas the radar inferences of ponded water lie within areas predicted to be thawed by modelling and radiostratigraphy. There is clear disagreement in certain areas, suggesting the presence of high geothermal flux anomalies.