Within a non-adiabatic dynamical method, we simulate charged polaron motion and dissociation in an organic molecule in the presence of dissipation. The dissipation, represented by damping, is introduced to investigate the influence of temperature on the mobility of carriers. We find that the velocity of the polaron has an inversely linear dependence on the damping, and hence the relationship between mobility and temperature is a power law, which is in agreement with the corresponding experiments. We also find that the velocity of the polaron exhibits a continuous dependence on the electric field in the presence of dissipation. In addition, we find that, in the presence of dissipation, the critical field that dissociates a polaron is reduced.