A key question in climate modeling is to what extent sea surface temperature and upper-ocean heat content are driven passively by air–sea heat fluxes, as opposed to forcing by ocean dynamics. This paper investigates the question using a climate model at different resolutions, and observations, for monthly variability. At the grid scale in a high-resolution climate model with resolved mesoscale ocean eddies, ocean dynamics (i.e., ocean heat flux convergence) dominates upper 50 m heat content variability over most of the globe. For deeper depths of integration to 400 m, the heat content variability at the grid scale is almost totally controlled by ocean heat flux convergence. However, a strong dependence on spatial scale is found—for the upper 50 m of ocean, after smoothing the data to around 7°, air–sea heat fluxes, augmented by Ekman heat transports, dominate. For deeper depths of integration to 400 m, the transition scale becomes larger and is above 10° in western boundary currents. Comparison of climate model results with observations show that the small-scale influence of ocean intrinsic variability is well captured by the high-resolution model but is missing from a comparable model with parameterized ocean-eddy effects. In the deep tropics, ocean dynamics dominates in all cases and all scales. In the subtropical gyres at large scales, air–sea heat fluxes play the biggest role. In the midlatitudes, at large scales >10°, atmosphere-driven air–sea heat fluxes and Ekman heat transport variability are the dominant processes except in the western boundary currents for the 400 m heat content.