  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. 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 $U(1)\times U(1)$.
