The role of changing vertical eddy heat flux on Southern Ocean heat uptake is investigated in an idealized eddy-permitting ocean model. Enhanced air-sea heat flux drives deep-reaching southern warming, due to a reduction in the isopycnal meridional temperature gradient and therefore decreased upward eddy heat flux. This mechanism is qualitatively similar in models with either permitted or parameterized eddies, due to its dependence on the isopycnal temperature gradient rather than the dynamical response of the eddy field. In contrast, increased wind stress drives mid-depth Southern Ocean cooling through an enhancement of the eddy field and resultant eddy heat divergence. The transient cooling extends over multiple decades while the mean flow adjusts to balance the faster eddy response. This wind-driven cooling mechanism has not been captured by coarse resolution models with fixed eddy parameterizations and is a possible candidate for the recent cooling observed in the Southern Ocean.