  The divergent perturbative expansion of the free-energy density of thermal
SU(3) gauge theory is resummed into a rapidly convergent series using a novel,
variational, implementation of the method of conformal mapping of the
corresponding Borel series. The resummed result differs significantly from
non-perturbative lattice simulations and the discrepancy is attributed to the
presence of a pole on the positive axis of the Borel plane. The position of
that pole is determined numerically and the difference between the lattice data
and the resummed series is related to a phenomenological bag `constant'.
