The Southern Ocean is a pivotal component of the global climate system yet it is poorly represented in climate models, with significant biases in upper-ocean temperatures, clouds and winds. Combining Atmospheric and Coupled Model Inter-comparison Project (AMIP5/CMIP5) simulations, with observations and equilibrium heat budget theory, we show that across the CMIP5 ensemble variations in sea surface temperature biases in the 40-60°S Southern Ocean are primarily caused by AMIP5 atmospheric model net surface flux bias variations, linked to cloud-related short-wave errors. Equilibration of the biases involves local coupled sea surface temperature bias feedbacks onto the surface heat flux components. In combination with wind feedbacks, these biases adversely modify upper-ocean thermal structure. Most AMIP5 atmospheric models that exhibit small net heat flux biases appear to achieve this through compensating errors. We demonstrate that targeted developments to cloud-related parameterisations provide a route to better represent the Southern Ocean in climate models and projections.