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Charge and heat transport through a single molecule tunnel-coupled toexternal normal electrodes have been studied. The molecule with sufficientlystrong interaction between lectrons and vibrational internal degrees of freedomcan be characterized by the negative effective charging energy U$<0$. Such amolecule has been considered and modeled by the Anderson Hamiltonian. Theelectrical conductance, thermopower and thermal conductance of the system havebeen calculated as a function of gate voltage in the weak coupling limit withinthe rate equation approach. In the linear regime the analytic formulae for thetransport coefficients in the pair dominated tunneling are presented. Theeffects found in the nonlinear transport include {\it inter alia} therectification of the heat current. The sense of forward (reverse) direction,however, depends on the tuning parameter and can be controlled by the gatevoltage. We also discuss the quantitation of the thermal conductance and thedepartures from the Wiedemann-Franz law.

Thermal transport of molecular junctions in the pair tunneling regime