To investigate the relationship between the thermal conductivity and the cooling rate, we have performed molecular-dynamics (MD) simulations based on a combination of the Langevin and Newton equations to deal with a heat transfer from l-Si to c-Si. The thermal conductivity of c-Si was measured by the direct method. In order to deal with finite-size effects, different cell sizes perpendicular to the direction of the heat current were used. The values of the thermal conductivity of 58 W/mK and 35.7 W/mK in the Tersoff potential were obtained at 1000 K and 1500 K, respectively. A MD cell with a length of 488.75 ¡Ê in the direction of a heat flow was used for estimating the natural cooling rate. The initial c/l interface systems were obtained by setting the temperatures of the MD cell at 1000 K and 1500 K, respectively, for Z <= 35 ¡Ê and 3800 K for Z > 35 ¡Ê. During the natural cooling processes, the temperature of the bottom 10 ¡Ê of the MD cell was controlled. The cooling rates of 7.4 × 1011 K/sec for 1000 K and 5.9 × 1011 K/sec for 1500 K were obtained, respectively.