Using the Kubo formula approach, we study the effect of electron interaction on thermal transport in the vicinity of a metal-insulator transition, with a granular metal as our model. For small values of dimensionless intergrain tunneling conductance, $gll1,$ we find that the thermal conductivity surprisingly shows a phonon-like algebraic decrease, $kappa(T)sim g^{2}T^{3}/E_{c}^{2}$ even though the electrical conductivity obeys an Arrhenius law, $sigma(T)sim ge^{-E_{c}/T};$ therefore the Wiedemann-Franz (WF) law is seriously violated. This violation arises from non-magnetic bosonic excitations of low energy that transport heat but not charge. Implications for experiment are discussed
