We consider a fluid close to its gas-liquid critical point in the Rayleigh-Bénard configuration. Owing to thermoacoustic effects, the bottom heating induces thermal boundary layers along both the lower and the upper horizontal plates. The hydrodynamic stability of these diffusing layers, whose bounding conditions are interchanged, is studied numerically in a two-dimensional (2D) approximation. As far as the convection onset criterion and the critical wave number are concerned, some discrepancies are found between the simulations and the predictions obtained by means of linear analysis. The extension of the study to three-dimensional configurations confirms the validity of the 2D approximation for the analysis of the hydrodynamic stability and shows its inadequacy when the layers become convection dominated.