We propose here that the Atlantic meridional overturning circulation (AMOC) plays an important role in setting the effective heat capacity of the World Ocean and thus impacts the pace of transient climate change. The depth and strength of AMOC are shown to be strongly correlated with the depth of heat storage across a suite of state-of-the-art general circulation models (GCMs). In those models with a deeper and stronger AMOC, a smaller portion of the heat anomaly remains in the ocean mixed layer, and consequently, the surface temperature response is delayed. Representations of AMOC differ vastly across the GCMs, providing a major source of intermodel spread in the sea surface temperature (SST) response. A two-layer model fit to the GCMs is used to demonstrate that the intermodel spread in SSTs due to variations in the ocean's effective heat capacity is significant but smaller than the spread due to climate feedbacks.