gluons is an essential key to the understanding of QCD and the occurrence of different phases which are expected to show up when going from low to high temperatures ($T$) and/or baryon number densities. For instance, at small or vanishing temperatures quarks and gluons get confined by the strong force while at high temperatures asymptotic freedom suggests a quite different QCD medium consisting of rather weakly coupled quarks and gluons, the so-called quark gluon plasma (QGP) [@PLP]. On quite general grounds it is therefore expected that the interactions get modified by temperature. For the analysis of these modifications of the strong forces the change in free energy due to the presence of a static quark anti-quark pair separated by a distance $r$ in a QCD-like thermal heat bath has often been used since the early work [@McLerran:1980pk; @McLerran:1981pb]. In fact, the static quark anti-quark free energy which is obtained from Polyakov loop correlation functions calculated at finite temperature plays a similar important role in the discussion of properties of the strong force as the static quark potential does at zero temperature.

The properties of this observable (at $T=0$: potential, at $T\neq0$: free energy) at short and intermediate distances ($rT\;\lsim\;1$) is 