  We present a model for the dynamics of current- and field-driven domain-wall
lines at nonzero temperature. We compute thermally-averaged drift velocities
from the Fokker-Planck equation that describes the nonzero-temperature dynamics
of the domain wall. As special limits of this general description, we describe
rigid domain walls as well as vortex domain walls. In these limits, we
determine also depinning times of the domain wall from an extrinsic pinning
potential. We compare our theory with previous theoretical and experimental
work.
