The rates and patterns of ocean heat storage and associated thermosteric sea level are influenced by ocean transport, such as mixing and large-scale circulation. However, existing climate models do not accurately capture the observed patterns of ocean warming and thermosteric sea level, with a large spread in their projections of ocean circulation and ocean heat uptake. Additionally, assessing the influence of ocean circulation changes on patterns of observed and simulated ocean warming remains a challenge. We will use a relationship between heat and carbon to reveal the effect of changes in ocean circulation from CO2 forcing on patterns of ocean warming in both observations and global Earth system models from the Fifth Coupled Model Intercomparison Project (CMIP5). We show that historical patterns of ocean warming are shaped by ocean heat redistribution, which CMIP5 models simulate poorly. However, we find that projected patterns of heat storage are primarily dictated by the pre-industrial ocean circulation (and small changes in unresolved ocean processes)—that is, by the patterns of added heat owing to ocean uptake of excess atmospheric heat rather than ocean warming by circulation changes. Climate models show more skill in simulating ocean heat storage by the pre-industrial circulation compared to heat redistribution, indicating that warming patterns of the ocean may become more predictable as the climate warms.