Six hydrographic basinwide sections, two in each of the three major ocean basins, are employed in a set of inverse calculations to determine the extent of exchange between the Pacific and Indian Oceans through the Indonesian Archipelago and the net global oceanic heat flux. All existing estimates of Indonesian Passage throughflow, including the largest (20 Sv), are consistent with the model constraints which combine data from the southern Pacific, Indian and Atlantic Oceans. The models and data are unable to limit the extent of the exchange, i.e., both smaller and larger throughflows produce physically reasonable circulation patterns. Seasonal and interannual variations, which have been found by other investigators and which are not resolved, suggest that in the long-term mean an estimate of about 10 Sv for the throughflow is most reasonable. Globally, at 30°S, the estimated net oceanic heat flux is −0.7 ± 0.1 PW (1 PW = 1015 W), dominated by a large (> 1 PW), southward flux in the Indian Ocean. Large equatorward heat flux values, O(0.8 PW), in the South Atlantic Basin are not consistent with the data. Therefore although the data are consistent with some water following the “warm water” return path for North Atlantic Deep Water (NADW), the “cold water” path must play the dominant role in the maintenance of the global thermohaline cell associated with the formation process of NADW.