Low dimensional and nanostructured materials have shown great potential to achieve higher thermoelectric figure-of-merit ZT than their bulk counterparts. One reason is their reduced thermal conductivities. The total thermal conductivity is composed of lattice thermal conductivity and the contribution from charge carriers. We study the charge transport of tall barrier superlattices in the cross-plane direction and the electronic thermal conductivity. The periodic potential barriers modify the electronic band structure and thus the charge and heat transport in superlattices are quite different from the bulk materials. The band edge profile changes with carrier concentration and temperature due to the charge transfer between wells and barriers. This is taken into account by a self-consistent solution of the coupled SchrOdinger and Poisson equations. Finally, the electrical conductivity and electronic thermal conductivity are calculated using the Boltzmann transport equation in superlattice miniband regime. It is shown that the Lorenz number, i.e., the ratio of electronic thermal conductivity to electrical conductivity, in the superlattice cross-plane direction deviates substantially from the Wiedemann-Franz law of bulk materials.