The source of the various planetary-period signals in Saturn’s magnetosphere is at present unknown. We investigate the possibility that the source of these signals is an axially asymmetric wind system in the thermosphere. We describe a feedback mechanism that has the potential to drive such axially asymmetric wind systems. The proposed mechanism relates thermospheric winds to heating from particle precipitation, via the generation of horizontal and field-aligned currents. The relevant physical processes are investigated using a highly simplified general circulation model of Saturn’s thermosphere and ionosphere. Our principal result is that the feedback mechanism is effective in permanently breaking the axial symmetry of the thermosphere, generating a drifting vortex-like structure at high latitudes. However, the precipitating electron energies required to power this structure are of the order of 5 MeV, 2–3 orders of magnitude greater than the observed auroral electron energies, and the highly axially asymmetric distribution of precipitation required across the polar regions of the planet is also inconsistent with observations. Despite these flaws, the model qualitatively explains several features of the observed variation in the pulsing of SKR emissions; in particular, the seasonal variation and the faster rotation rate in the winter hemisphere. We cannot reproduce the apparent 7 month lag in the response of the Saturn Kilometric Radiation (SKR) rotation rate to seasonal variation, but instead suggest the possibility that this effect may have its origin in long chemical time-scales in the upper atmosphere. We also predict the possible existence of secondary periodic features in the SKR emissions with periods of ∼15 planetary rotations, driven by complex wave behaviour in the thermosphere.