  We study thermal conductivity in the disordered two-dimensional electron
liquid in the presence of long-range Coulomb interactions. We describe a
microscopic analysis of the problem using as a starting point the partition
function defined on the Keldysh contour. We extend the Renormalization Group
(RG) analysis developed for thermal transport in the disordered Fermi liquid,
and include scattering processes induced by the long-range Coulomb interaction
in the sub-temperature energy range. For the thermal conductivity, unlike for
the electric conductivity, these scattering processes yield a logarithmic
correction which may compete with the RG-corrections. The interest in this
correction arises from the fact that it violates the Wiedemann-Franz law. We
checked that the sub-temperature correction to the thermal conductivity is not
modified, neither by the inclusion of Fermi liquid interaction amplitudes nor
as a result of the RG flow. We thereby expect that the answer obtained for this
correction is final. We use the theory to describe thermal transport on the
metallic side of the metal-insulator transition in Si MOSFETs.
