Geothermal heat flow in the polar regions plays a crucial role in understanding ice-sheet dynamics and predictions of sea level rise. Continental-scale indirect estimates often have a low spatial resolution and yield largest discrepancies in West Antarctica. Here we analyse geophysical data to estimate geothermal heat flow in the Amundsen Sea Sector of West Antarctica. With Curie depth analysis based on a new magnetic anomaly grid compilation, we reveal variations in lithospheric thermal gradients. We show that the rapidly retreating Thwaites and Pope glaciers in particular are underlain by areas of largely elevated geothermal heat flow, which relates to the tectonic and magmatic history of the West Antarctic Rift System in this region. Our results imply that the behavior of this vulnerable sector of the West Antarctic Ice Sheet is strongly coupled to the dynamics of the underlying lithosphere.