To study the role of the Atlantic meridional overturning circulation (AMOC) in climate change, we perform an abrupt CO2–doubling experiment using a coupled atmosphere-ocean- ice model with a simple geometry that separates the ocean into small and large basins. As in observations and high-end climate models, the small basin exhibits a MOC and warms at a faster rate than the large basin. In our set-up, this contrast in heat storage rates is 0.6 ± 0.1 W/m^2, and we argue that this is due to the small basin MOC. However, the MOC weakens significantly, yet this has little impact on the small basin’s heat storage rate. We find this is due to the effects of both compensating warming patterns and interbasin heat transports. Thus, although the presence of a MOC is important for enhanced heat storage, MOC weakening is surprisingly unimportant.