= Solution
The <Wiedemann-Franz law> applies to a normal degenerate <metal> when the same itinerant <Electrons> carry heat and charge, scattering is approximately elastic over the thermal shell, and the transport probability varies slowly across the energy interval $k_BT$ around the <Fermi level>. The comparison uses the electronic <thermal conductivity> $K_e$, with any lattice contribution removed.
It works particularly well as $T\to0$ when elastic impurity or defect scattering dominates. It also often holds approximately for $\Theta_D\ll T\ll T_F$, where thermally populated <phonons> act as a nearly elastic classical scattering field. Room temperature need not lie above the <Debye temperature> for every metal.
At intermediate temperatures, inelastic small-angle <electron-phonon scattering> can relax heat much more efficiently than charge. Then $\tau_Q\ne\tau_\sigma$ and $K_e/(\sigma T)$ can be smaller than $L_0$. Strong energy dependence of scattering, additional neutral heat carriers, or a transition out of the normal metallic state also invalidates the simple derivation. An observed deviation alone does not identify which assumption failed.
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