Ocean warming patterns are a primary control on regional sea level rise and transient climate sensitivity. However, controls on these patterns in both observations and models are not fully understood, complicated as they are by their dual dependence on the “addition” of heat to the ocean’s interior along background ventilation pathways and on the “redistribution” of heat between regions by changing ocean dynamics. While many previous studies attribute heat redistribution to changes in high-latitude processes, here we propose that substantial heat redistribution is explained by the large-scale adjustment of the geostrophic flow to warming within the pycnocline. We explore this hypothesis in the University of Victoria Earth System Model, estimating added heat using the the Transport Matrix Method. We find that throughout the mid-latitudes, subtropics and tropics, patterns of added and redistributed heat in the model are strongly anti-correlated (R ≈ −0.75). We argue this occurs because changes in the ocean currents, acting across pre-existing temperature gradients, redistribute heat away from regions of strong passive heat convergence. Over broad scales, this advective response can be estimated from changes in upper ocean density alone using the thermal wind relation and is linked to an adjustment of the subtropical pycnocline. These results highlight a previously unappreciated relationship between added and redistributed heat and emphasize the role that subtropical and mid-latitude dynamics play in setting patterns of ocean heat storage.