We present a study of the linear hydrodynamic stability of purely conductive Poiseuille flow in three-dimensional horizontal rectangular channels uniformly heated from below. Its originality is to modellize the flow using realistic conditions on all the boundaries of the channel, in particular, no-slip conditions on the vertical lateral boundaries. The aim of this paper is to provide quantitative results for the values of the critical dimensionless parameters. When the Rayleigh number Ra is higher than the critical value Ra*, the instabilities are shown to be three-dimensional horseshoe-shaped transversal rolls for Reynolds numbers Re smaller than the critical value Re*, and longitudinal rolls for Re > Re*. The results are given for a wide range of the Prandtl number (10(-6) less than or equal to Pr less than or equal to 10(5)) and of the transversal aspect ratio B of the duct (0.1 less than or equal to B less than or equal to 5.4 and B --> infinity).