We derive a covariant equation for the motion of the extended charge and show how a consistent description is achieved for nonrelativistic velocities. If the external force is generated by the classical stochastic zero-point electromagnetic field, the equation of motion has the form of a Langevin equation with memory. The memory function is due to radiation reaction and is related to the charge density, which we have assumed to be spherically symmetric and rigid only in the nonrelativistic limit. The extension of our results to finite temperature is briefly discussed for the cases of free and harmonically bounded nonrelativistic motions.