  We analyze a two dimensional SU(3) gauge model of Wilson lines as a
dimensionally reduced model of high temperature QCD_3. In contrast to
perturbative dimensional reduction it has an explicit global Z(3) symmetry in
the action. The phase diagram of the model is studied in the space of two free
parameters used to describe the self interaction of the Wilson lines. In
addition to the confinement-deconfinement transition, the model also exhibits a
new Z(3)-breaking phase. These findings are obtained by numerical simulations,
and supported by a perturbative calculation to one loop. A screening mass from
Polyakov loop correlations is calculated numerically. It matches the known
QCD_3 mass in a domain of parameters belonging to the normal deconfined phase.
