  Numerical modeling is used to investigate the dynamics of a polaron in a
chain with small random Langevin-like perturbations which imitate the
environmental temperature $T$ and under the influence of a constant electric
field. In the semiclassical Holstein model the region of existence of polarons
in the thermodynamic equilibrium state depends not only on temperature but also
on the chain length. Therefore when we compute dynamics from initial polaron
data, the mean displacement of the charge mass center differs for
different-length chains at the same temperature. For a large radius polaron, it
is shown numerically that the ``mean polaron displacement'' (which takes
account only of the polaron peak and its position) behaves similarly for
different-length chains during the time when the polaron persists. A similar
slope of the polaron displacement enables one to find the polaron mean velocity
and, by analogy with the charge mobility, assess the ``polaron mobility''. The
calculated values of the polaron mobility for $T \approx 0$ are close to the
value at $T=0$, which is small but not zero. For the parameters corresponding
to the small radius polaron, simulations of dynamics demonstrate switching mode
between immobile polaron and delocalized state. The position of the new polaron
is not related to the position of the previous one; charge transfer occurs in
the delocalized state.
