This paper addresses the problem of the discrepancy between experimental and numerical studies which is generally observed concerning the central thermal stratification in air-filled differentially heated cavities at high Rayleigh number. To this aim, large eddy simulations of turbulent natural convection flow are first validated on the basis of the spectral simulations data provided by the Part I article (Sergent et al., 2013). Then, three sets of simulations are considered at RaH = 1.5 × 109, which differ by the type of imposed thermal boundary conditions at the end walls. It is thereby shown that the complete set of experimental temperature distribution is required to recover full agreement between numerical and experimental results; purely convective adiabatic conditions as well as periodic conditions fail to reproduce the global 3D flow structure. In the Part III article ( Xin et al., 2012), it is shown that this temperature distribution results from a complete 3D convection-conduction-radiation coupling at the cavity walls.