The temperature profile around the moving solid-liquid interface during non-equilibrium molecular dynamics (MD) simulations of crystallization and melting is examined for HCP Mg and BCC Fe. An evident spike (valley) is found around the solid-liquid interface during solidification (melting). Considering the effect of a non-uniform temperature distribution, it is found that, if the actual interface temperature is adopted to compute the interface mobility, rather than the thermostat temperature (or the mean temperature of the whole system), the kinetic coefficient is approximately a factor of two larger than previous estimates. Although the magnitude of the kinetic coefficient is larger than the previous estimates, the crystalline anisotropies derived in the current work are consistent with earlier calculations. (C) 2010 Elsevier B.V. All rights reserved.