It has been suggested that a slowdown of the Atlantic meridional overturning cell (AMOC) would cause the Northern Hemisphere to cool by a few degrees. We use a sequence of simple analytical models to show that due to the nonlinearity of the system, the simplified heat flux from the modeled AMOC to the atmosphere above is so robust that even changes of as much as 50% in the present AMOC transport are not enough to significantly change the temperature of the outgoing warmed atmosphere (i.e., the fraction of the atmosphere warmed by the AMOC). Our most realistic model (which is still a far cry from reality) 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. The behavior of the system is attributable to four key aspects of the underlying physical processes: (1) convective atmospheric transport increases by warming the atmosphere, (2) the ocean is warmer than the atmosphere, (3) the surface heat flux is usually proportional to the temperature difference between the ocean and the atmosphere, and (4) the specific heat capacity of water is much larger than that of the air. Taken together, these properties of the system lead to the existence of a dynamic “asymptotic” state, a modeled regime, in which even significant changes in the AMOC transport have almost no effect on the ocean-atmosphere heat flux and the resulting outgoing atmospheric temperature. In the hypothetical limit of an infinitely large specific heat capacity of water, Cpw there is no change in either the atmospheric transport or the temperatures of the ocean and the atmosphere, regardless of how large the reduction in the AMOC transport is. Although our models may be too simple to allow for a direct application to the ocean and atmosphere, they do shed light on the processes in question.