Climate models show a wide range of southern hemispheric jet responses to greenhouse gas forcing. One approach to constrain the future jet response is by utilising the fluctuation–dissipation theorem (FDT) which links the forced response to internal variability timescales, with the Southern Annular Mode (SAM) the most dominant mode of variability of the southern hemispheric jet. We show that interannual stratospheric variability approximately doubles the SAM timescale during austral summer in both re-analysis data and models from the Coupled Model Intercomparison Project, Phases 5 (CMIP5) and 6 (CMIP6). Using a simple barotropic model, we demonstrate how the enhanced SAM timescale subsequently leads to an overestimate of the forced jet response based on the FDT, and we introduce a method to correct for the stratospheric influence. This result helps to resolve a previously identified discrepancy between the seasonality of jet response and the internal variability timescale. However, even after accounting for this influence, the SAM timescale cannot explain inter-model differences in the forced jet shift across CMIP models during austral summer.