Freely propagating and counterflow laminar premixed steady hydrogen/air and methane/air flames are investigated numerically using complex chemistry and detailed transport models. All the transport coefficients in the mixture, including thermal diffusion coefficients, are evaluated using cost-effective, accurate algorithms derived recently by the authors from the kinetic theory of gases. Our numerical results provide a quantitative assessment of the impact of thermal diffusion on planar flame speed as a function of equivalence ratio and on extinction limits of counterflow flames as a function of either strain rate or equivalence ratio. In some cases, such as rich hydrogen/air flames, the effect of thermal diffusion is actually opposite to the one expected from a qualitative viewpoint or obtained with empirical models. In addition, we observe relevant effects of thermal diffusion on extinction of methane/air counterflow flames