Abstract A simple linearized transport model of anomalous Southern Ocean sea surface temperature (SST) is studied to determine whether it can sustain anomalies of realistic amplitudes under a physically based stochastic forcing. As noted in previous studies, eigenmodes of this system with zonal wavenumbers 2 and 3 share key propagation characteristics with the SST anomalies associated with the Antarctic Circumpolar Wave (ACW). The system is solved on a grid that follows the path of the Antarctic Circumpolar Current (ACC) and is forced by a stochastic heat flux. The forcing is white in space and time and represents the advection of the mean SST gradient by high-frequency variations in the cross-ACC velocity, due to mesoscale eddy variability. The magnitude of the stochastic forcing is determined from a global eddy-permitting ocean model. Anomalous ocean surface velocity variability (8 cm s−1) coupled to a mean cross-ACC SST gradient of 0.8°C (°latitude)−1 sustains anomalous interannual SST variability at low wavenumbers and amplitudes of the order of 1°C, consistent with those associated with the ACW. In the long-term mean, variance is broadly spread among low wavenumbers, in contrast to the dominance of one or two zonal wavenumbers in the ACW observations. It is found, however, that the model produces single dominant wavenumbers over individual periods of decades, suggesting that the apparent unimodal nature of the ACW may be an artifact of the short observational record used to infer it. Alternatively, it is shown that a nonisotropic forcing may also result in a stronger preference for particular zonal wavenumbers. It is shown that if the atmosphere at mid to high southern latitudes has an equivalent barotropic response to heating, then the resulting sea level pressure anomalies reproduce the phase relationship of the observed ACW. These results are consistent with the notion that a simple stochastically forced advection of SST anomalies can explain SST variability associated with the ACW to leading order.