It is now well established that changes in the X-ray spectral state of black hole low-mass X-ray binaries are correlated with changes in the radio properties of those systems. Assuming radio power is a proxy for jet power, we can say that the jet is continuously present in the hard state and undetectable (and therefore weaker) in the soft state. Since the different accretion states are also generally assumed to be associated with different disc geometries – the hard state with a hot, thick flow, and the soft state with a cold, thin disc – we investigate the possibility that these two phenomena are linked; i.e. the difference in disc geometry is the cause of the difference in observed jet power. We do this by comparing various measures of jet power in numerical simulations of accretion discs of differing temperatures and thicknesses. We perform these simulations using the general relativistic magnetohydrodynamic code cosmos++ and a newly added cooling function, which allows us to regulate the disc scale height H/r at different radii. We find no apparent correlation between the disc scale height and jet power whenever we normalize the latter by the mass accretion history of each simulation. We attribute this result to the role that the ‘corona’ plays in confining and accelerating the jet (our corona may also be considered a failed magnetohydrodynamic ‘wind’). The properties of the corona do not vary significantly from one simulation to another, even though the scale heights of the discs vary by up to a factor of 4. If this holds true in nature, then it suggests that the correlation between spectral state and jet power must be attributable to some other property, possibly the topology of the magnetic field. Alternatively, it could be that the corona disappears altogether in the soft state, which would be consistent with observations, but has so far not been seen in simulations.