This paper presents the results of a numerical study on the unsteady three-dimensional natural convection of a power-law fluid in a thick walled vessel being driven by natural heat convection in the surrounding air inside a cubical cavity. Continuity, linear momentum and energy equations for the internal Otswald the Waele shear thinning fluid, with a power index n = 0.4, are used to describe fluid mechanics and natural heat transfer along the conjugate continuity, Navier Stokes and energy equations for the external Newtonian air flow and the transient heat diffusion equation in the walls of the inner fluid container. Unsteady 3D thermal convection of the inner shear-thinning fluid, with n = 0.4, is analyzed in comparison with the fluid mechanics and heat transfer results for the Newtonian fluid, with n = 1, for two values of the Rayleigh number: Ra = 2.09 x 10(4) and 2.09 x 10(6). Thermo-physical properties of the inner fluid are allowed to change with temperature for the two values of the Rayleigh number and for both the Newtonian and the power law non-Newtonian inner fluids. Numerical simulations were carried out by an-in house- Fortran 90 Finite Volume Method parallelized code. Results of the evolution of the fluid mechanics are described in terms of the streamlines and those related to the unsteady convective heat transfer in terms of the isotherms. (C) 2016 Elsevier Masson SAS. All rights reserved.