The importance of the Jovian thermosphere with regard to magnetosphere–ionosphere coupling is often neglected in magnetospheric physics. We present the first study to investigate the response of the Jovian thermosphere to transient variations in solar wind dynamic pressure, using an azimuthally symmetric global circulation model coupled to a simple magnetosphere and fixed auroral conductivity model. In our simulations, the Jovian magnetosphere encounters a solar wind shock or rarefaction region and is subsequently compressed or expanded. We present the ensuing response of the coupling currents, thermospheric flows, heating and cooling terms, and the aurora to these transient events. Transient compressions cause the reversal, with respect to steady state, of magnetosphere–ionosphere coupling currents and momentum transfer between the thermosphere and magnetosphere. They also cause at least a factor of two increase in the Joule heating rate. Ion drag significantly changes the kinetic energy of the thermospheric neutrals depending on whether the magnetosphere is compressed or expanded. Local temperature variations appear between View the MathML source~−45and175K for the compression scenario and View the MathML source~−20and50K for the expansion case. Extended regions of equatorward flow develop in the wake of compression events – we discuss the implications of this behaviour for global energy transport. Both compressions and expansions lead to a View the MathML source~2000TW increase in the total power dissipated or deposited in the thermosphere. In terms of auroral processes, transient compressions increase main oval UV emission by a factor of ~4.5~4.5 whilst transient expansions increase this main emission by a more modest 37%. Both types of transient event cause shifts in the position of the main oval, of up to 1° latitude.