In this study, we present the behavior of free convective heat transfer in a rectangular cavity by two entirely different scales of numerical methods, namely a mesoscale and macroscale methods. The cavity is bounded by two vertical isothermal walls kept at different temperatures and by two horizontal perfectly conducting walls. The heat flow simulations were carried out across the two isothermal walls by varying the aspect ratio of cavity with six different values -0.2, 0.5, 1.5, 2.0, 2.5 and 3.0. The macroscale simulations were performed by solving the Navier-Stokes equation using finite difference scheme while the mesoscale simulations were done using lattice Boltzmann method. This study found that the heat transfer mechanism, fluid flow behavior in terms of formation, size and strength of vortex are critically depending on the aspect ratio of the geometry. Numerical results also show excellent agreement between these two scales of simulations.