important for the understanding of in-medium modifications of heavy quark bound states. A quantitative analysis of heavy quark free energies becomes of considerable importance for the discussion of possible signals for the quark gluon plasma formation in heavy ion collision experiments [@Matsui:1986dk; @RR]. For instance, recent studies of heavy quarkonium systems within potential models use the quark anti-quark free energy to define an appropriate finite temperature potential which is considered in the non-relativistic Schrödinger equation [@Digal:2001iu; @Digal:2001ue; @Wong:2001kn; @Wong:2001uu]. Such calculations, however, do not quite match the results of direct lattice calculations of the quarkonium dissociation temperatures which have been obtained so far only for the pure gauge theory [@Datta:2003ww; @Asakawa:2003re]. It was pointed out [@Kaczmarek:2002mc] that the free energy ($F$) of a static quark anti-quark pair can be separated into two contributions, the internal energy ($U$) and the entropy ($S$). The separation of the entropy contribution from the free energy, [*i.e.*]{} the variable $U=F+TS$, could define an appropriate effective potential at finite temperature[^1] [@Kaczmarek:2002mc; @Zantow:2003ui], $V_{\text{eff}}(r,T)\equiv
U$, to be used as input in model calculations and might explain in parts the quantitative differences found when comparing solutions of the Schrödinger equation with direct calculations of spectral functions [@Datta:2003ww; @Asakawa:2003re]. 