  We investigate the effect of vibrational degrees of freedom on the linear
thermoelectric transport through a single-level quantum dot described by the
spinless Anderson-Holstein impurity model. To study the effects of strong
electron-phonon coupling, we use the nonperturbative numerical renormalization
group approach. We also compare our results, at weak to intermediate coupling,
with those obtained by employing the functional renormalization group method,
finding good agreement in this parameter regime. When applying a gate voltage
at finite temperatures, the inelastic scattering processes, induced by
phonon-assisted tunneling, result in an interesting interplay between
electrical and thermal transport. We explore different parameter regimes and
identify situations for which the thermoelectric power as well as the
dimensionless figure of merit are significantly enhanced via a Mahan-Sofo type
of mechanism. We show, in particular, that this occurs at strong
electron-phonon coupling and in the antiadiabatic regime.
