The response of the atmospheric boundary layer to fronts of sea surface temperature (SST) is characterized by reduction of wind speed over warm SST, and a tight correlation between curl and divergence of the wind stress and the down- and crosswind components of the SST gradient, respectively. The associate regression (or coupling) coefficients for the wind stress divergence are consistently larger than those for the wind stress curl. To explore the underlying physics we introduce a linear model of the atmospheric boundary response to SST fronts in the presence of background advection. The model includes modulation by gradients of SST of boundary layer hydrostatic pressure and vertical mixing, and of the impact of secondary circulation on stratification aloft of the boundary layer. The model solutions are a strong function of the scale of the SST and the background advection, and recover observed characteristics. We discuss the processes underlying the distinct coupling coefficients for wind stress curl and divergence. The latter is dominated by non-rotational sea-breeze, while the former is governed by geostrophic spin-down.