  The gluon transverse self-energy of the pure Yang-Mills system at
high-temperature is analysed in the static limit and at fourth order in the
coupling. Possible contributions to this function are collected, seen to be
gauge-fixing independent subsets and shown to vanish all, except those which
are either regulators or constituents of the self-energy of Euklidean 3D
Yang-Mills theory at zero temperature. The latter self-energy, in turn, is
known from the non-perturbative analysis by Karabali and Nair.
