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.