A model due to Eshelby for computing the drag force upon an abrupt kink moving at low velocity through a phonon gas and its extension to include the effect of the finite width of the kink are analyzed in detail. The temperature dependence of the drag force is derived and is shown to be in reasonable agreement with earlier qualitative predictions made by Lothe. This force is related to the dislocation viscous damping coefficient appearing in the string model of dislocation motion. In this form the theory is compared with recent experimental results. Good agreement is found if the kink width (in units of the appropriate Burgers vector) is ∼4 or 1 in Cu and Al, respectively. An incidental problem in attempting to unify the theory with that of the Bordoni peak is also discussed briefly.