We have previously shown simulation results for centrifugally driven plasma convection in Saturn’s inner magnetosphere (2 < L < 12) using the Rice Convection Model, including a continuously active distributed plasma source, and the effects of the Coriolis force and the pickup current. These simulations result in a quasi-steady state, in which fast, narrow inflow channels alternate with slower, wider outflow channels, consistent with Cassini Plasma Spectrometer observations. These previous simulations, however, did not include the plasma pressure. We investigate here the effects of finite plasma pressure and the associated gradient-curvature drift current by giving the cold plasma a finite temperature. Our simulations confirm the theoretical expectation that a finite plasma pressure produces a force in the positive radial direction, the same direction as the centrifugal force, and acts as an additional driver of plasma convection. Our simulations also confirm that the radial velocities can be reduced (to keep them within observational constraints) by increasing the assumed ionospheric Pedersen conductance (also within observational constraints).