  We calculate the electrical and thermal conductivity of a two-dimensional
electron gas with strong spin--orbit coupling in which the scattering is
dominated by electron--electron collisions. Despite the apparent absence of
Galilean invariance in the system, the two-particle scattering does not affect
the electrical conductivity above the band-crossing point where both helicity
bands are filled. Below the band-crossing point where one helicity band is
empty, switching on the electron--electron scattering leads only to a limited
decrease of the electrical conductivity, so that its high-temperature value is
independent of the scattering intensity. In contrast to this, thermal
conductivity is not strongly affected by the spin-orbit coupling and exhibits
only a kink as the Fermi level passes through the band-crossing point.
