Ocean models are used to investigate how variations in surface heat fluxes and ocean heat transports contribute to variations of tropical Atlantic SSTs on decadal timescales. The observed patterns of variability, deduced from reanalyses of the National Centers for Environmental Prediction (NCEP), are found to involve the ocean’s response to variations in the strength of the northeast and southeast trades. Stronger trade winds are associated with anomalously cool surface temperatures. The trade winds and surface temperatures in each hemisphere appear to behave independently but each is associated with anomalous cross-equatorial flow. A numerical model is used in an attempt to simulate this variability. The model is an ocean general circulation model coupled to a simple model of the atmospheric mixed layer and is forced by NCEP winds from 1958 to 1998. The model reasonably reproduces the observed variability. Analysis of the ocean model’s mixed layer energy budget shows that, on decadal timescales, the surface temperature variability is forced by the changes in surface fluxes and is damped by changes in the ocean heat transport. The changes in ocean heat transport are dominated by the horizontal advection of anomalous temperatures by the mean meridional currents. If advection of the mean SST field by anomalous currents is neglected, then the history of observed surface temperatures can still be adequately represented. If advection of the anomalous SSTs by the mean circulation is also neglected, then the model significantly overestimates the surface temperature anomalies but reproduces their temporal evolution. In the more complete models, between 158N and 158S, the changes in ocean heat transport are largely in phase with the changes in surface heat fluxes and SST. Evidence for ocean heat transport either leading or lagging development of surface temperature anomalies is weak in the deep Tropics but appears more persuasive in the northern subtropics. Consistent with these findings, SST anomalies are largely stationary in the deep Tropics but appear to propagate poleward in the northern subtropics. Nonetheless these results suggest that the role of the ocean in tropical Atlantic decadal climate variability is largely passive and damping. Differences with other models that show a more critical role for the ocean, and relevance to reality, are discussed.