  The linear thermoelectric properties of molecular junctions are theoretically
studied close to room temperature within a model including electron-electron
and electron-vibration interactions on the molecule. A nonequilibrium adiabatic
approach is generalized to include large Coulomb repulsion through a
self-consistent procedure and applied to the investigation of large molecules,
such as fullerenes, within the Coulomb blockade regime. The focus is on the
phonon thermal conductance which is quite sensitive to the effects of strong
electron-electron interactions within the intermediate electron-vibration
coupling regime. The electron-vibration interaction enhances the phonon and
electron thermal conductance, and it reduces the charge conductance and the
thermopower inducing a decrease of the thermoelectric figure of merit. For
realistic values of junction parameters, the peak values of the thermoelectric
figure of merit are still of the order of unity since the phonon thermal
conductance can be even smaller than the electron counterpart.
