Abstract Tropical stratospheric aerosol injections are known to strengthen the wintertime Stratospheric Polar Vortex (SPV). Here, we revisit the circulation response to aerosol perturbations during the first month following injection using chemistry‐climate model simulations of regional nuclear war scenarios. We diagnose the atmospheric heat and momentum budgets to assess the thermal and dynamical responses to tropical soot injection. The results reveal that, during the initial adjustment period of 30 days, radiative heating from aerosols is confined to the tropics. In contrast, temperature and circulation changes in the mid‐to‐high latitudes are governed primarily by dynamical processes, with changes in eddy momentum fluxes driving the intensification of the SPV. Together, these findings demonstrate that circulation responses to stratospheric aerosol perturbations—through the redistribution of heat and momentum to remote regions—play a key role in the strengthening of the winter polar jet.