  We derive asymptotically exact expressions for the thermopower and figure of
merit of a quantum impurity connecting two noninteracting leads in the linear
response regime where the chemical potential and temperature differences
between the leads are small. Based on sum rules for the single-particle
impurity spectral function, these expressions become exact at high temperatures
as well as in the very strongly correlated regime, where the impurity Coulomb
repulsion is much larger than the temperature. Although modest interactions
impede thermoelectric performance, a very large Coulomb scale restores the
optimal transport properties of noninteracting electrons, albeit renormalized
to account for the absence of double occupancy in the impurity. As with
noninteracting electrons, the electronic contribution to the figure of merit is
limited only by the spectral broadening that arises from the coupling between
the impurity and the leads.
