The influence of the overturning circulation on the anthropogenic carbon sink in the North Atlantic is investigated with a simple box model. The net air-sea flux of anthropogenic carbon in the North Atlantic is the result of two opposing fluxes: The first is the uptake caused by the disequilibrium between the rapidly rising atmospheric pCO2 and the dissolved carbon content in the ocean, depending mainly on the water exchange rate between mixed layer and interior North Atlantic ocean. Superimposed is a second flux, related to the northward transport of heat within the Atlantic basin, that is directed out of the ocean, contrary to conventional wisdom. It is caused by a latitudinal gradient in the ratio of seawater alkalinity to total dissolved inorganic carbon that in turn is related to the cooling and freshening of surface water on its way north. This flux depends strongly on the vertical structure of the upper branch of the overturning circulation and on the distribution of undersaturation and supersaturation of CO2 in Atlantic surface waters. A data-based estimate of anthropogenic carbon inventory in the North Atlantic is consistent with a dominance of the disequilibrium flux over the heat-flux-related outgassing at the present time, but, in our model, does not place a strong constraint on the net anthropogenic air-sea flux. Stabilization of the atmospheric pCO2 on a higher level will change the relative role of the two opposing fluxes, making the North Atlantic a source of anthropogenic carbon to the atmosphere. We discuss implications for the interpretation of numerical carbon cycle models.