We investigate the effects of sea surface temperature (SST)-dependent wind stress on the wind-driven quasigeostrophic (QG) double gyre. The main effects are to reduce the strength of the circulation and to shift the inter-gyre jet to the south. The SST front across the inter-gyre jet induces a zonal wind stress anomaly over the jet that accelerates the southern flank of the jet and decelerates the northern flank. This local wind stress anomaly causes the jet to shift southwards. Shifting the jet south, away from the peak wind stress, reduces the net power input to the ocean circulation. Allowing the wind stress to depend on the difference between the atmospheric and oceanic velocity also reduces the net wind power input, and has a larger impact than SST dependence. When wind stress depends only on SST, the impact on the circulation is stronger than when wind stress depends on both SST and ocean surface velocity. Ocean surface velocity dependence leads to direct extraction of mesoscale energy by the winds. In contrast, SST dependence leads to injection (extraction) of mesoscale energy in the subtropical (subpolar) gyres, with almost complete cancellation because of the symmetric wind field.