  We calculate thermal transport in the Falicov-Kimball model on an
infinite-coordination-number Bethe lattice. We perform numerical calculations
of the thermoelectric characteristics and concentrate on finding materials
parameters for which the electronic thermoelectric figure-of-merit ZT is large,
suggesting potential cooling and power generation applications. Surprisingly,
the Bethe lattice has significant qualitative and quantitative differences with
the previously studied hypercubic lattice. At low temperature it is unlikely
that these systems can be employed in thermoelectric devices due to the low
conductivities and due to a larger lattice contribution to the thermal
conductivity $\kappa_L$, but at high temperature, the thermoelectric parameters
appear more promising for devices due to a significant enhancement of ZT and a
smaller relative contribution by the lattice thermal conductivity.
