We present a new method to identify and track intrinsic point defects in a silicon crystal in a molecular dynamics simulation. If the canonical ensemble is employed, the resulting trajectory can be used to compute the diffusion coefficients of defects for a prescribed temperature. A fit of these values for different temperatures to an Arrhenius-type function gives the temperature dependence of the diffusion coefficient over the whole range of interest. For this purpose, we performed simulations employing the Stillinger-Weber potential as well as the Tersoff potential. We were able to improve the accuracy of the approximation of the diffusion coefficients for self-interstitials and vacancies computed by Sinno (1998) and Tang et al. (1997).