  We study to what extent the three-dimensional SU(N)+adjoint Higgs theory can
be used as an effective theory for finite temperature SU(N) gauge theory, with
N=2,3. The parameters of the 3d theory are computed in 2-loop perturbation
theory in terms of T/Lambda_MSbar,N,N_f. The perturbative effective potential
of the 3d theory is computed to two loops for N=2. While the Z(N) symmetry
probably driving the 4d confinement-deconfinement phase transition (for N_f=0)
is not explicit in the effective Lagrangian, it is partly reinstated by
radiative effects in the 3d theory. Lattice simulations in the 3d theory are
carried out for N=2, and the static screening masses relevant for the
high-temperature phase of the 4d theory are measured. In particular, we measure
non-perturbatively the O(g^2 T) correction to the Debye screening mass. We find
that non-perturbative effects are much larger in the SU(2) + adjoint Higgs
theory than in the SU(2) + fundamental Higgs theory.
