  Because of asymptotic freedom, QCD becomes weakly interacting at high
temperature: this is the reason for the transition to a deconfined phase in
Yang-Mills theory at temperature $T_c$. At high temperature $T \gg T_c$, the
smallness of the running coupling $g$ induces a hierachy betwen the "hard",
"soft" and "ultrasoft" energy scales $T$, $g T$ and $g^2 T$. This hierarchy
allows for a very successful effective treatment where the "hard" and the
"soft" modes are successively integrated out. However, it is not clear how high
a temperature is necessary to achieve such a scale hierarchy.
  By numerical simulations, we show that the required temperatures are
extremely high. Thus, the quantitative success of the effective theory down to
temperatures of a few $T_c$ appears surprising a posteriori.
