Recent studies using atmospheric general circulation models forced by the observed time history of global sea surface temperature anomalies have been used to hind-cast the temporal history of the North Atlantic Oscillation. They find that the mean of a large ensemble of integrations using slightly different initial atmospheric conditions reproduces the observed variability surprisingly well, especially on time scales longer than a few years. However, they also find that amplitude of the atmospheric variability is considerably reduced and the air-sea heat fluxes are of the reverse sign to those observed. Here, a linear model of midlatitude atmosphere/ocean interaction forced only by high-frequency atmospheric stochastic variability is shown to reproduce all of these findings. This model suggests that despite the hind-cast skill, the useful predictability associated with midlatitude SST anomalies may be limited to one or two seasons.