Despite global warming, SSTs in the Southern Ocean (SO) have cooled in recent decades largely as a result of internal variability. The global impact of this cooling is assessed by nudging evolving SO SST anomalies to observations in an ensemble of coupled climate model simulations under historical radiative forcing, and comparing against a control ensemble. The most significant remote response to observed SO cooling is found in the tropical South Atlantic, where increased clouds and strengthened trade winds cool the sea surface, partially offsetting the radiatively-forced warming trend. The SO ensemble produces a more realistic tropical South Atlantic SST trend, and exhibits a higher pattern correlation with observed SST trends in the greater Atlantic basin, compared to the control ensemble. SO cooling also produces a significant increase in Antarctic sea ice, but not enough to offset radiatively-induced ice loss; thus, the SO ensemble remains biased in its sea ice trends.