The diffusion of adsorbed Si dimers on the reconstructed Si(001) surface is studied using molecular dynamics and a recently developed environment-dependent tight binding potential. The simulations are performed at 1300 K. 163 K below the experimental temperature at which the p(2 x 1) surface reconstruction is lost. Different initial conditions have been considered in each of the 63 simulations, giving a total simulation time of 5748 ps. At this temperature Si ad-dimers are still able to diffuse as a unit, without dissociation. We have found three different pathways for diffusion between the top of the dimer rows and the trough. One of them was already predicted by low temperature studies and the other two, are activated at high temperature contributing to make the diffusion less anisotropic.