In this part of the paper we consider the effect of the thermal motion of the atoms on the dynamics of a moving dislocation in the linear chain model. We express the effect in terms of a thermal drag force averaged over a lattice step. We compute this drag force for a range of dislocation velocities through computer simulation single-step runs. In each of such runs we compute the change of dislocation velocity caused by a fluctuation of velocity or displacement in one of the atoms. We then add up the overall effect according to thermal equilibrium statistics. We employ a first-order approximation in the sense that we take the thermal drag force to be proportional to the temperature. Our analysis is thus limited to the low-temperature range. For a range of dislocation velocities we obtain a negative thermal drag force (as anticipated by Weiner from a normal-mode analysis). The magnitude of the thermal effect is such that it causes a 10−4 change in dislocation velocity along a single lattice step per degree Kelvin (at low temperature levels).