Here we study the effect of non-Boussinesq effects on hydrothermal convection in porous media. This work is motivated by post-impact hydrothermal convection in the Chicxulub impact crater in Yucat´an, Mexico. Post-impact hydrothermal simulation experiences very large temperature differences and significant changes in fluid properties. Studies of convection commonly employ the Boussinesq approximation which neglects density changes everywhere except the buoyancy term. To study the effect of this approximation in the presence of large density differences we compare convective fluxes from numerical simulations with and without the Boussinesq approximation. This study delves into the influence of temperature-dependent density on hydrothermal flow within porous media, drawing inspiration from the temperature profiles observed in the Chicxulub crater. These profiles showcase significant temperature variations, prompting the proposal of a non-Boussinesq approximation for the model. The weak formulation for the adimensional model is derived and finite element spaces are chosen according to the involved continuous spaces. Finally, we present numerical simulations using FEniCS for our new approach and the results are compared with the classical Boussinesq approximation.