We discuss the first heat flow measurements taken in the Atlantic section of the Antarctic Ocean. The one value from the Scotia Sea is compatible with the youthful age proposed for this sea. The values around the American-Antarctica ridge are low and scattered as expected from regions of rough topography and variable sediment cover. The values from the well sedimented western Weddell Sea are surprisingly high for a deep, isostatically adjusted sedimentary basin, and decrease to the Southeast. Such high heat flow could result from a marginal basin type origin or be related to a large difference in age across the Sea.