  We derive the partition function for the SU(3) Yang-Mills theory in the
presence of a uniform gluon field within the background field method. We show,
that the $n$-body gluon contributions in the partition function are
characterized solely by the Polyakov loop. We express the effective action
through characters of different representations of the color gauge group
resulting in a form deduced in the strong-coupling expansion. A striking
feature of this potential is that at low temperature gluons are physically
disfavored and therefore they do not yield the correct thermodynamics. We
suggest a hybrid approach to Yang-Mills thermodynamics, combining the effective
gluon potential with glueballs implemented as dilaton fields.
