Multiple integrations of an atmospheric general circulation model (AGCM) exhibit differences in the decadal mean of the surface heat flux, Q. The differences (typically 2-3 Wm-2 can be as large as 10 Wm-2) in places, which are shown to produce sea-surface temperature (SST) changes up to approximately 0.5°C in a hybrid coupled atmosphere/ocean sea ice model or HCM. This underscores a significant mechanism by which long-lived SST anomalies can arise, independent of any internal ocean variability, for which there is very little predictive capability. Consequently, AGCM integrations using prescribed SSTs provide upper bounds on the predictability of atmospheric variability. The HCM is used to estimate the magnitude of the drift in the climatology of coupled models if flux adjustments are based on AGCM integrations of decadal duration. The random interannual fluctuations in Q averaged over the ocean are most closely associated with fluctuations in surface latent heating and long wave radiation to space. The same fluctuations are not associated with land surface variability. The impact of variability in other fluxes on SST in the HCM was also analyzed. Changes due to wind-stress were approximately half those due to heating, while changes due to freshwater forcing were relatively unimportant except at polar latitudes.