A set of Direct Numerical Simulations in a heated square cavity invoking the Boussinesq approximation was carried out at Rayleigh numbers ranging between 10(8) and 10(11) and Prandtl number of 0.71. The three dimensional configurations studied represent an infinitely deep cavity, thus corresponding to a statistically two-dimensional flow with an imposed temperature varying linearly on the horizontal walls. In such configuration, the Rayleigh number, and therefore turbulence intensity, is the highest ever reached. The database presented herein includes first and second order statistical moments as well as full Reynolds stresses, turbulent heat fluxes and temperature variance budgets. The latter are extremely rare for buoyancy driven flow configurations and are therefore believed to be valuable to the turbulence modelling community. The analysis of the data collected thus focuses on aspects of relevance to the Reynolds averaged modelling of such flows. The effect of increasing the Rayleigh number on the flow statistics, Nusselt number predictions and thermal stratification is investigated. The most important aspect influencing the behaviour of the budgets was found to be the displacement of the position of the maximum of temperature variance towards the inner zone of the boundary layer. Such difference in behaviour between the thermal and velocity boundary layers introduces regions of negative production in the budgets that tend to increase with the Rayleigh number. The production of turbulence by buoyancy is also found to be of the same order of magnitude as other budget terms at all Rayleigh numbers. (C) 2018 Elsevier Ltd. All rights reserved.