  The thermodynamical properties of a pure Yang-Mills theory SU(N) is described
by a gas of gluonic quasiparticles with temperature dependent mass $m(T)$ and a
bag function $B(T).$ The analytic behavior of $m(T)$ and the pressure $p$ at
high $T$ are derived and constraints on the parameters defining $B(T)$ are
discussed. The trace anomaly $\theta=\rho-3p$ is evaluated in the high $T$
domain: it is dominated by a quadratic behavior $\theta =nKT^{2},$ where
$n=2(N^{2}-1)$ is the number of degrees of freedom and $K$ is an integration
constant which does not depend on the bag function $B(T)$. This is a general
result which is in very good agreement with recent lattice simulations.
