  A general discussion of the ratio of thermal and electrical conductivities in
non-Fermi liquid metals is given. In metals with sharp Drude peaks, the
relevant physics is correctly organized around the slow relaxation of
almost-conserved momenta. While in Fermi liquids both currents and momenta
relax slowly, due to the weakness of interactions among low energy excitations,
in strongly interacting non-Fermi liquids typically only momenta relax slowly.
It follows that the conductivities of such non-Fermi liquids are obtained
within a fundamentally different kinematics to Fermi liquids. Among these
strongly interacting non-Fermi liquids we distinguish cases with only one
almost-conserved momentum, which we term hydrodynamic metals, and with many
patchwise almost-conserved momenta. For all these cases, we obtain universal
expressions for the ratio of conductivities that violate the Wiedemann-Franz
law. We further discuss the case in which long-lived `cold' quasiparticles, in
general with unconventional scattering rates, coexist with strongly interacting
hot spots, lines or bands. For these cases, we characterize circumstances under
which non-Fermi liquid transport, in particular a linear in temperature
resistivity, is and is not compatible with the Wiedemann-Franz law. We suggest
the likely outcome of future transport experiments on CeCoIn5, YbRh2Si2 and
Sr3Ru2O7 at their critical magnetic fields.
