The effect of the Southern Ocean on global climate change is assessed using Earth system model projections following an idealized 1% annual rise in atmospheric CO2. For this scenario, the Southern Ocean plays a significant role in sequestering heat and anthropogenic carbon, accounting for 40% ± 5% of heat uptake and 44% ± 2% of anthropogenic carbon uptake over the global ocean (with the Southern Ocean defined as south of 36°S). This Southern Ocean fraction of global heat uptake is however less than in historical scenarios with marked hemispheric contrasts in radiative forcing. For this idealized scenario, inter-model differences in global and Southern Ocean heat uptake are strongly affected by physical feedbacks, especially cloud feedbacks over the globe and surface albedo feedbacks from sea-ice loss in high latitudes, through the top-of-the-atmosphere energy balance. The ocean carbon response is similar in most models with carbon storage increasing from rising atmospheric CO2, but weakly decreasing from climate change with competing ventilation and biological contributions over the Southern Ocean. The Southern Ocean affects a global climate metric, the transient climate response to emissions, accounting for 28% of its thermal contribution through its physical climate feedbacks and heat uptake, and so affects inter-model differences in meeting warming targets. This article is part of a discussion meeting issue 'Heat and carbon uptake in the Southern Ocean: the state of the art and future priorities'.