We study a thermohaline system in which the density gradients arise from salinity and temperature differences. Such systems arise in e.g. geological waste storage and geothermal energy exploitation. A sedimentary-basin set-up is investigated where salinity and temperature increase with depth. In such systems, the buoyancy forces caused by salinity and temperature gradients give rise to counter-acting convection cells. The homogenization theory ideas from Held et al. (2005) are applied to the solute and heat transport equations and the two resulting cell problems solved with the coupling between the heat and solute transport preserved. A dimensionless number whose sign changes to negative when thermal-convection is predominant is derived from the solutions to the cell problems in terms of physical variables. The number is tested against numerical simulations performed with the software package d³f on sufficiently refined grids that deliver stable numerical solutions without upwind techniques.