  We calculate the energy current flowing in the bulk of a (2+1)-dimensional
system of massive Dirac fermions and along a (1+1)-dimensional domain wall
generated by flipping the sign of the particle mass. We show that, at low
temperatures and in the long-wavelenghth limit, the system does not support a
bulk thermal Hall current proportional to the temperature gradient. The only
such contribution is due to states localised at the domain wall. This puts an
end to a controversy existing in the literature and amends previous results
obtained via first-order perturbation calculations.
