By injecting SO2 into the stratosphere at four latitudes (30°, 15° N/S), it might be possible not only to reduce global mean surface temperature but also to minimize changes in the equator-to-pole and inter-hemispheric gradients of temperature, further reducing some of the impacts arising from climate change relative to equatorial injection. This can happen only if the aerosols are transported to higher latitudes by the stratospheric circulation, ensuring that a greater part of the solar radiation is reflected back to space at higher latitudes, compensating for the reduced sunlight. However, the stratospheric heating produced by these aerosols modifies the circulation and strengthens the stratospheric polar vortex which acts as a barrier to the transport of air toward the poles. We show how the heating results in a feedback where increasing injection rates lead to stronger high-latitudinal transport barriers. This implies a potential limitation in the high-latitude aerosol burden and subsequent cooling.