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