  A Feynman-Jensen version of the thermal variational principle is applied to
hot gauge fields, Abelian as well as non-Abelian: scalar electrodynamics
(without scalar self-coupling) and the gluon plasma. The perturbatively known
self-energies are shown to derive by variation from a free quadratic
(''Gaussian'') trial Lagrangian. Independence of the covariant gauge fixing
parameter is reached (within the order $g^3$ studied) after a reformulation of
the partition function such that it depends on only even powers of the gauge
field. Also static properties (Debye screening) are reproduced this way. But
because of the present need to expand the variational functional, the method
falls short of its potential nonperturbative power.
