From first-principles approaches, we investigate the thermoelectric efficiency of a molecular junction where a benzene molecule is connected directly to the platinum electrodes. We calculate the thermoelectric figure of merit ZT in the presence of electronvibration interactions with and without local heating under two scenarios: linear response and finite bias regimes. In the linear response regime, ZT saturates around the electrode temperature T e=25K in the elastic case, while in the inelastic case we observe a non-saturated and a much larger ZT beyond T e=25K attributed to the tail of the FermiDirac distribution. In the finite bias regime, the inelastic effects reveal the signatures of the molecular vibrations in the low-temperature regime. The normal modes exhibiting structures in the inelastic profile are characterized by large components of atomic vibrations along the current density direction on top of each individual atom. In all cases, the inclusion of local heating leads to a higher wire temperature T w and thus magnifies further the influence of the electronvibration interactions due to the increased number of local phonons.