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We calculate the electronic contribution to the thermal conductance in aquantum dot that is weakly coupled via tunnel barriers to two electronsreservoirs. A linear response model is derived for the calculation of the heatcurrent Q through the quantum dot when a small temperature difference and asmall voltage difference are applied between the two reservoirs. We find thatthe thermal conductance oscillates as a function of the Fermi energy. Theperiodicity of these oscillations is the same as this of the Coulomb blockadeoscillations of the conductance. In the quantum limit the peak values of thethermal conductance tends to zero as exp(-DE/kT) where DE is the spacingbetween the energy levels in the dot. This surprising result implies thefailure of the Wiedemann-Franz law in the quantum limit and it could lead tostructures with large figure of merit ZT. We have also examined the behavior ofthe thermal conductance in the classical limit and we find that theWiedemann-Franz is recovered.Comment: 10 pages, 4 figures, v3: more references added and discussed, some  typos correcte

Thermal conductance of a weakly coupled quantum dot