Our most realistic model involves a warm ocean losing heat to an otherwise motionless and colder atmosphere. As a result, the compressible atmosphere convects and the generated airflow ultimately penetrates horizontally into the surrounding air. There are four key aspects of the process: (i) the non-linear dependence of the atmospheric mass transport on the oceanic mass transport, (ii) the dependence of the atmospheric transport on the large specific heat capacity ratio of water to air (~4), (iii) the fact that the ocean is warmer (by 10-20 degrees) than the air, and (iv) bulk formulas imply that the heat flux is proportional to the temperature difference between the ocean and the air. The four aspects lead the system to a dynamical saturation state where even significant changes in the AMOC transport have almost no effect on both the ocean/air heat flux and the resulting outgoing atmospheric temperature. In the hypothetical limit of infinitely large specific heat capacity of water, there is no change in either the atmospheric transport or the temperatures of the ocean and the atmosphere, regardless how large the reduction in the AMOC transport is.