The three-dimensional natural convection in a cubical cavity is revisited using the theoretical formulation without introducing the usual approximations. Particular interests are focused on the Rayleigh numbers ranging around transition to chaos, i.e. Ra=O(108). It is found that the Boussinesq approximation, which was commonly used in the study of natural convection, indeed leads to some noticeable errors in the investigated Ra Range. The errors stemmed from another common approximation of neglecting the viscous dissipation term in the energy equation are investigated too. Finally, evolution of the buoyancy-driven flow in a cubical cavity from transition to chaos is performed using the exact, three-dimensional formulation.