  We study the thermal conductivity of the disordered two-dimensional electron
gas. To this end we analyze the heat density-heat density correlation function
concentrating on the scattering processes induced by the Coulomb interaction in
the sub-temperature energy range. These scattering processes are at the origin
of logarithmic corrections violating the Wiedemann-Franz law. Special care is
devoted to the definition of the heat density in the presence of the long-range
Coulomb interaction. To clarify the structure of the correlation function, we
present details of a perturbative calculation. While the conservation of energy
strongly constrains the general form of the heat density-heat density
correlation function, the balance of various terms turns out to be rather
different from that for the correlation functions of other conserved quantities
such as the density-density or spin density-spin density correlation function.
