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The ratio of global mean surface air temperature change to cumulative CO2 emissions, referred to as transient climate response to cumulative CO2 emissions (TCRE), has been shown to be approximately constant on centennial time scales. The mechanisms behind this constancy are not well understood, but previous studies suggest that compensating effects of ocean heat and carbon fluxes, which are governed by the same ocean mixing processes, could be one cause for this approximate constancy. This hypothesis is investigated by forcing different versions of the University of Victoria Earth System Climate Model, which differ in the ocean mixing parameterization, with an idealized scenario of 1% annually increasing atmospheric CO2 until quadrupling of the preindustrial CO2 concentration and constant concentration thereafter. The relationship between surface air warming and cumulative emissions remains close to linear, but the TCRE varies between model versions, spanning the range of 1.2 degrees-2.1 degrees CEgC(-1) at the time of CO2 doubling. For all model versions, the TCRE is not constant over time while atmospheric CO2 concentrations increase. It is constant after atmospheric CO2 stabilizes at 1120 ppm, because of compensating changes in temperature sensitivity (temperature change per unit radiative forcing) and cumulative airborne fraction. The TCRE remains approximately constant over time even if temperature sensitivity, determined by ocean heat flux, and cumulative airborne fraction, determined by ocean carbon flux, are taken from different model versions with different ocean mixing settings. This can partially be explained with temperature sensitivity and cumulative airborne fraction following similar trajectories, which suggests ocean heat and carbon fluxes scale approximately linearly with changes in vertical mixing.