Antarctica is the largest reservoir of ice on Earth. Understanding its ice sheet dynamics is crucial to unraveling past global climate change and making robust climatic and sea level predictions. Of the basic parameters that shape and control ice flow, the most poorly known is geothermal heat flux. Direct observations of heat flux are difficult to obtain in Antarctica, and until now continent-wide heat flux maps have only been derived from low-resolution satellite magnetic and seismological data. We present a high-resolution heat flux map and associated uncertainty derived from spectral analysis of the most advanced continental compilation of airborne magnetic data. Small-scale spatial variability and features consistent with known geology are better reproduced than in previous models, between 36% and 50%. Our high-resolution heat flux map and its uncertainty distribution provide an important new boundary condition to be used in studies on future subglacial hydrology, ice sheet dynamics, and sea level change.