Natural convective heat transfer across a horizontal rectangular enclosure containing air whose horizontal bottom surface is heated and whose upper surface is cooled and whose side surfaces are adiabatic has been considered. In some practical situations involving this type of flow the upper surface is inclined at a small angle to the horizontal. The present study was undertaken to determine how significant is the effect of the inclination angle on the heat transfer rate across the enclosure. Enclosures with aspect ratios of between 4 and 8 and top surface angles of inclination of between 0° and 7.5° have been considered. It has been assumed that flow is steady, laminar, and two-dimensional and the Boussinesq approach has been adopted. The solution has been obtained using the commercial solver ANSYS FLUENT^©. The mean heat transfer rate from the bottom heated surface has been expressed in terms of Nusselt numbers based on the mean distance between the lower and upper surfaces, the Nusselt numbers being dependent on the Rayleigh number, on the aspect ratio, on the upper surface inclination angle and on the Prandtl number. Since only the case where the enclosure contains air has been considered, results have been obtained for a Prandtl number of 0.7. Rayleigh numbers between 10² and 10⁸ have been considered. The results obtained show that for smaller angles of top surface inclination the inclination angle has a very small effect on the heat transfer rate.