  We investigate an effect that an ideal Lorenz number $L_{\rm i}$ of
correlated metal shows peculiar Fermi surface dependence, which is caused by
the onset of a particular channel of Umklapp scattering. We evaluate $L_{\rm
i}$ for some simple models and transition metals, and note that $L_{\rm i}$ for
Na$_x$CoO$_2$ decreases sensitively as $x$ approaches an Umklapp threshold
around $x_c \simeq 0.6$.
