  Thermally reduced QCD leads to three dimensional SU(3) gaugefields coupled to
an adjoint scalar field $A_0$. We compute the effective potential in the
one-loop approximation and evaluate the VEV's of $TrA_0^2$ and $TrA_0^3$. In
the Higgs phase not only the former, but also the latter has a VEV. This
happens where the SU(3) gauge symmetry is broken minimally with U(2) still
unbroken. The VEV of the cubic invariant breaks charge conjugation and CP. It
is plausible that in the Higgs phase one has a transition for large enough
Higgs selfcoupling to a region where $TrA_0^3$ has no VEV and where the
gaugesymmetry is broken maximally to $U(1)\times U(1)$. For a number of colours
larger than 3 an even richer phase structure is possible.
