Abstract Climate change in the Southern Hemisphere (SH) polar stratosphere is associated with substantial changes in the atmospheric circulation that extend to the earth’s surface. The mechanisms that drive the changes in the SH troposphere are not fully understood, but most previous hypotheses have focused on the role of atmospheric dynamics rather than that of radiation. This study quantifies the radiative response of temperatures in the SH polar troposphere to the forcing from long-term temperature and ozone trends in the SH polar stratosphere. A novel methodology is employed that explicitly neglects changes in tropospheric dynamics and hence isolates the component of the tropospheric temperature response that is radiatively driven by the overlying stratospheric trends. The results reveal that both the amplitude and seasonality of the observed cooling of the middle and upper SH polar troposphere over the past few decades are consistent with a reduction in downwelling longwave radiation induced by cooling in the SH polar stratosphere. The results are compared with analogous calculations for trends in the Northern Hemisphere (NH) polar stratosphere. Both the observations and radiative calculations imply that the comparatively weak trends in the NH polar stratosphere have not played a central role in driving NH tropospheric climate change. Overall, the results suggest that radiative processes play a key role in coupling the large trends in SH polar stratospheric temperatures to tropospheric levels. The tropospheric radiative temperature response documented here could be important for triggering the changes in internal tropospheric dynamics associated with stratosphere–troposphere coupling.