  We study the high-temperature phase of SU(2) and SU(3) QCD using lattice
simulations of an effective 3-dimensional SU(N) + adjoint Higgs -theory,
obtained through dimensional reduction. We investigate the phase diagram of the
3D theory, and find that the high-T QCD phase corresponds to the metastable
symmetric phase of the 3D theory. We measure the Debye screening mass m_D with
gauge invariant operators; in particular we determine the O(g^2) and O(g^3)
corrections to m_D. The corrections are seen to be large, modifying the
standard power-counting hierarchy in high temperature QCD.
