We analyze the sensitivity of the oceanic thermohaline circulation (THC) regarding perturbations in fresh water flux for a range of coupled oceanic general circulation - atmospheric energy balance models. The energy balance model (EBM) predicts surface air temperature and fresh water flux and contains the feedbacks due to meridional transports of sensible and latent heat. In the coupled system we examine a negative perturbation in run-off into the southern ocean and analyze the role of changed atmospheric heat transports and fresh water flux. With mixed boundary conditions (fixed air temperature and fixed surface fresh water fluxes) the response is characterized by a completely different oceanic heat transport than in the reference case. On the other hand, the surface heat flux remains roughly constant when the air temperature can adjust in a model where no anomalous atmospheric transports are allowed. This gives an artificially stable system with nearly unchanged oceanic heat transport. However, if meridional heat transports in the atmosphere are included, the sensitivity of the system lies between the two extreme cases. We find that changes in fresh water flux are unimportant for the THC in the coupled system.