Adding thin compartmental plates near the internal walls of enclosures has been numerically modeled using the lattice Boltzmann method. This practice was found to be an effective way to further suppress the disadvantageous effects of heat leak, along with the application of insulation materials on the external surfaces. A modified extrapolation scheme for handling the thermal boundary of the thin plate was proposed and verified by comparison with the conventional coupled boundary scheme. The simulation of the natural convection during the cooling down processes and at steady states in the enclosure indicates that the existence of the plates leads to a higher cooling rate and a more favorable temperature uniformity. For a typical case, the one with plates takes 6% less time to reach the halfway point of the steady state and has 26% less temperature variance. Effects by the plates' positions and sizes were parametrically investigated, in order to find an optimal geometrical configuration. In addition, the fluid's intrinsic characteristics and the relative heat leak by using the Rayleigh number and Nusselt number, respectively, have been discussed in detail through hydrodynamic and convective heat transfer analyses.