With active convection in a reservoir, regions of upflow in convective systems can increase the geothermal energy potential of said reservoir; on the other hand, convection introduces uncertainty, because it is difficult to locate these regions of upflow. Several predictive criteria, such as the Rayleigh number, exist to estimate whether convection might occur under certain conditions. Once a convection system is established, diagnostic measures are needed for describing the convection pattern, e.g. the likely number of upwelling regions. We use the thermodynamic measure called entropy production to describe the influence of spatially heterogeneous permeability on a hydrothermal convection pattern in a hot sedimentary aquifer in the Perth Basin, Australia. To this end, we analyze the entropy production in multiple ensembles in a Monte Carlo study. Each ensemble contains several hundred realizations of spatially heterogeneous permeability. By observing the measure of entropy production, we see that the convection patterns in our models drastically change with the introduction and increase of a finite correlation length in permeability. An initial decrease of the average entropy production number with increasing lateral correlation length indicates that less ensemble members show convection. When neglecting the purely conductive ensembles in our analysis, no change in the convection pattern is seen for lateral correlation lengths larger 2000 m. Besides model dimensions, our results show that also the spatial anisotropy of important flow-parameters, such as permeability, is important to be considered if hydrothermal convection is likely to occur in a sedimentary geothermal reservoir system.