Previous work has demonstrated that observed and modeled climates show a near-time-invariant ratio of mean land to mean ocean surface temperature change under transient and equilibrium global warming. This study confirms this in a range of atmospheric models coupled to perturbed sea surface temperatures (SSTs), slab (thermodynamics only) oceans, and a fully coupled ocean. Away from equilibrium, it is found that the atmospheric processes that maintain the ratio cause a land-to-ocean heat transport anomaly that can be approximated using a two-box energy balance model. When climate is forced by increasing atmospheric CO2 concentration, the heat transport anomaly moves heat from land to ocean, constraining the land to warm in step with the ocean surface, despite the small heat capacity of the land. The heat transport anomaly is strongly related to the top-of-atmosphere radiative flux imbalance, and hence it tends to a small value as equilibrium is approached. In contrast, when climate is forced by prescribing changes in SSTs, the heat transport anomaly replaces “missing” radiative forcing over land by moving heat from ocean to land, warming the land surface. The heat transport anomaly remains substantial in steady state. These results are consistent with earlier studies that found that both land and ocean surface temperature changes may be approximated as local responses to global mean radiative forcing. The modeled heat transport anomaly has large impacts on surface heat fluxes but small impacts on precipitation, circulation, and cloud radiative forcing compared with the impacts of surface temperature change. No substantial nonlinearities are found in these atmospheric variables when the effects of forcing and surface temperature change are added.