The electrical conductivity, the thermoelectric power, and the electrical contribution to the thermal conductivity of quantum wire superlattices have been studied. The effects of tunneling through the barriers due to finite potential off-sets and of the thermal currents through the barrier layers are shown to be essential to describe properly the thermoelectric figure of merit of realistic quantum wire superlattices. The figure of merit exhibits a maximum as a function of superlattice period which, for large barrier off-sets, is found to be substantially enhanced over that for the bulk material and also larger than that for quantum well superlattices.