In this paper, natural convection of non-Newtonian molten polymer in a cavity with a sinusoidal heated wall has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The molten polymer is modeled on power-law non-Newtonian fluid. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105) and power-law index (n = 0.5-1.5). Results indicate that the innovative FDLBM is an appropriate method for the problem. The augmentation of the power-law index causes heat transfer to drop generally. Moreover, the alteration of power-law index influences the heat transfer at Ra = 105 more than Ra = 10 4 although the difference is marginal.