  The thermodynamics of $SU(2)$ Yang-Mills theory in the covariant variational
approach is studied by relating the free action density in the background of a
non-trivial Polyakov loop to the pressure of the gluon plasma. The correct
subtraction of the vacuum contribution in the free action density is argued
for. The Poisson resummed expression for the pressure can be evaluated
analytically in limiting cases, and shows the correct Stefan-Boltzmann limit at
$T \to \infty$, while the limit $T \to 0$ is afflicted by artifacts due to
massless modes in the confined phase. Several remedies to remove these
artifacts are discussed. Using the numerical $T=0$ solutions for the ghost and
gluon propagators in the covariant variational approach as input, the pressure,
energy density and interaction strength are calculated and compared to lattice
data.
