Anthropogenic carbon emissions increase the atmospheric CO2 and lead to surface warming. The ocean mitigates this climate response through the uptake of heat and carbon. At the same time, surface warming and changes in atmospheric CO2 modify the ocean carbon uptake through changes in the ocean ventilation (e.g., circulation and stratification) and biogeochemistry (e.g., acidification, changes in solubility) leading to a further effect on the climate response through these feedback mechanisms. To explore this link between the ocean and the climate response we invoke an ocean carbon cycle feedback framework representing the ocean carbon uptake in terms of a dependence on atmospheric CO2 and surface temperature changes, the latter providing a crude representation of physical effects of climate change. The control of the different processes on the ocean carbon cycle feedbacks (biology, chemistry, ventilation) and ultimately on the climate response is investigated using a conceptual atmosphere-ocean model and a suite of realistic Earth system models integrated for 1% annual rise in atmospheric CO2. Particularly, we focus on the relative contribution from a range of physical processes including the effect of the mixed-layer thickness and the strength of the meridional overturning circulation on the ocean carbon cycle feedbacks.