The present study concerns an air-filled differentially heated cavity of 1 m × 0.32 m × 1 m (width × depth × height) subject to a temperature difference of 15 K and is motivated by the need to understand the persistent discrepancy observed between numerical and experimental results on thermal stratification in the cavity core. An improved experiment with enhanced metrology was set up and experimental data have been obtained along with the characteristics of the surfaces and materials used. Experimental temperature distributions on the passive walls have been introduced in numerical simulations in order to provide a faithful prediction of experimental data. By means of DNS using spectral methods, heat conduction in the insulating material is first coupled with natural convection in the cavity. As heat conduction influences only the temperature distribution on the top and bottom surfaces and in the near wall regions, surface radiation is added to the coupling of natural convection with heat conduction. The temperature distribution in the cavity is strongly affected by the polycarbonate front and rear walls of the cavity, which are almost black surfaces for low temperature radiation, and also other low emissivity walls. The thermal stratification is considerably weakened by surface radiation. Good agreement between numerical simulations and experiments is observed on both time-averaged fields and turbulent statistics. Treating the full conduction-convection-radiation coupling allowed to confirm that experimental wall temperatures resulted from the coupled phenomena and this is another way to predict correctly the experimental results in the cavity.