We present a theory of the temperature and electric field dependence on the mobility of polarons in conjugated polymers in terms of a tight-binding and stochastic approach. The polaron mobility is shown to have a strong dependence on the electric field, with two distinct regimes of temperature dependence. Lattice thermal oscillations enhance polaron mean velocity for electric fields of 1.0 mV/angstrom or higher. In contrast, its mobility is damped by thermal oscillations under weaker electric fields. This semiconductor/metallic analogous behavior comes from the difference between the inertial content acquired by polarons under stronger/weaker electric fields. These new results and their analysis shed new light on several experimental controversies.