Flow of undersaturated water in limestone aquifer can cause continuous permeability growth due to dissolution. We have simulated the evolution of permeability field of a 3-D porous limestone aquifer subjected to geothermal temperature gradient and vertical through-flow. The upward flow through porous limestone results in dissolution since calcite is a retrograde soluble mineral. In addition to permeability growth by promoting more dissolution, through-flow also inhibits Rayleigh Benard convection. To understand the temporal evolution of permeability and flow fields, we have performed several simulations with various combinations of initial permeability and through-flow magnitude. Since our computational domain is different in size and boundary conditions from past studies related to buoyant convection in porous medium, we have carried out simulations without reactive alteration to distinguish the hydrothermal systems as stable or unstable. The permeability growth is insignificant in the central part of the reservoir as the temperature gradient vanishes due to forced convection. Permeability growth is more near the edges, where temperature gradients are significant due to conductive heat transfer from the boundaries. For small magnitudes of through-flow, convection rolls are formed near the corners. However, the growth is very localized and rolls never form when magnitude of through-flow is large.