A three-dimensional numerical simulation is carried out to investigate the natural convection in a shallow wedge subject to solar radiation. The study reveals three distinct stages of the flow development from an isothermal and stationary state: an initial stage, a transitional stage and a quasi-steady stage. The heat transfer at the initial stage is dominated by conduction from the sloping bottom. The transitional stage starts with the onset of instabilities, and the quasi-steady state is characterised by steady growth of a spatially averaged temperature. The present results have confirmed the earlier observations in a flow visualisation experiment and a two-dimensional simulation.