Summary: The model proposed by A. Postelnicu et al. [Int. Commun. Heat Mass Transf. 26, No. 8, 1183–1191 (1999; doi:10.1016/S0735-1933(99)00108-6); ibid. 27, No. 5, 729–738 (2000; doi:10.1016/S0735-1933(00)00153-6)] for the natural convection boundary-layer flow on a vertical surface in a porous medium driven by spatially-dependent localised internal heating is discussed further. Their results for a prescribed wall temperature characterised by the parameter \(\lambda\) are extended to a consideration of the singularity seen in the solution as \(\lambda\rightarrow-\frac{1}{2}\) and to the asymptotic limit \(\lambda\rightarrow\infty \), where convection resulting from the wall temperature becomes more important near the wall and showing a region of reversed flow/temperatures below ambient away from the wall. The case, not treated by Postelnicu et al. [loc. cit.], when there is a prescribed surface heat flux is also treated, finding that the solution became singular as \(\lambda\rightarrow-\frac{1}{3}\), the nature of which is discussed. The large \(\lambda\) limit is also obtained again finding that the dominant effect is the convection resulting from the wall heat transfer though here the temperature within the boundary layer remains above ambient.