  We study thermal transport in the disordered Fermi liquid at low
temperatures. Gravitational potentials are used as sources for finding the heat
density and its correlation function. For a comprehensive study, we extend the
renormalization group (RG) analysis developed for electric transport by
including the gravitational potentials into the RG scheme. Our analysis reveals
that the Wiedemann-Franz law remains valid even in the presence of quantum
corrections caused by the interplay of diffusion modes and the electron
electron interaction. In the present scheme this fundamental relation is
closely connected with a fixed point in the multi-parametric RG-flow of the
gravitational potentials.
