The article describes numerical investigations of turbulent natural convection of air flow in an inclined square cavity with a hot wavy wall. The focus is on studying the effect of the inclination angle and the amplitude of the undulation on the turbulent heat transfer. After reviewing literature in Sect. 1, a description of the physical problem set-up (Sect. 2) and its mathematical formulation (Sect. 3), general comments on the numerical procedures employed are given in Sect. 4. Before considering the cavity with the undulated hot wall, low Reynolds number \(k-\varepsilon\), \(k-\omega\), \(k-\omega\) SST RANS models (using FLUENT) and a coarse DNS (SATURNE Code) are tested for a simpler model problem for which experimental data is available. Based on the outcome of this pre-study, the \(k-\omega\) SST model appears to be best suited to numerically solve the problem of turbulent natural convection of air flow in an inclined square cavity with a hot wavy wall (Sect. 5) The behavior of the proposed numerical method is investigated, among others, by evaluating it on different grids. Emphasis is placed on values of temperature, Nusselt number, velocities and turbulent viscosity for Rayleigh numbers up to \(Ra=10^{12}\) (Sect. 6). Sect. 7 summarizes the conclusions, adequate references are given.