Ocean warming may lead to smaller body sizes of marine ectotherms, because metabolic rates increase exponentially with temperature while the capacity of the cardiorespiratory system to match enhanced oxygen demands is limited. Here, we explore the impact of rising sea water temperatures on Atlantic cod (Gadus morhua), an economically important fish species. We focus on changes in the temperature-dependent growth potential by a transfer function model combining growth observations with climate model ensemble temperatures. Growth potential is expressed in terms of asymptotic body weight and depends on water temperature. We consider changes between the periods 1985–2004 and 2081–2100, assuming that future sea water temperatures will evolve according to climate projections for IPCC AR5 scenario RCP8.5. Our model projects a response of Atlantic cod to future warming, differentiated according to ocean regions, leading to increases of asymptotic weight in the Barents Sea, while weights are projected to decline at the southern margin of the biogeographic range. Southern spawning areas will disappear due to thermal limitation of spawning stages. These projections match the currently observed biogeographic shifts and the temperature- and oxygen-dependent decline in routine aerobic scope at southern distribution limits.