The convective heat transfer in a homogeneous porous duct of rectangular cross section in a horizontal orientation is examined. The flow is modeled by the Darcy equation and an averaged, single-equation model is used for the heat transfer. The aspect ratio of the duct (γ = a/b) appears as the natural geometrical parameter and the Rayleigh number Ra, which is the product of the Grashof number and the Prandtl number, appears as the natural dynamical parameter. Uniqueness of the solution at low values of Ra is demonstrated. The complete structure of the symmetric and asymmetric stationary solutions is traced numerically up to values of Ra of about 10 000, using arclength continuation. The limit points and the symmetry breaking bifurcation points are calculated numerically by using the appropriate extended system formulations. The manner in which these singular points unfold is examined as the aspect ratio is varied over 0.6≤γ≤1.4. Determination of linear stability shows that branches of stationary solutions above a Ra of about 4100 are unstable to arbitrary perturbations. The origin of a curve of Hopf points on one of the fold curves is detected around Ra = 6560, γ = 1.365.