Ansatz deduced in Eq. (\[t=0ansatz\]). We again show in this figure the results from $SU(3)$-lattice (thick line) and perturbative (dashed line) calculations at zero temperature from [@Necco:2001gh; @Necco:2001xg]. The strong $r$-dependence of the running coupling near $T_c$ observed already in pure gauge theory [@Kaczmarek:2004gv] is also visible in 2-flavor QCD. Although our data for 2-flavor QCD do not allow for a detailed quantitative analysis of the running coupling at smaller distances, the qualitative behavior is in quite good agreement with the recent quenched results. At large distances the running coupling shows a strong temperature dependence which sets in at shorter separations with increasing temperature. At temperatures close but above $T_c$, $\alpha_{qq}(r,T)$ coincides with $\alpha_{qq}(r)$ already at separations $r\;\simeq\;0.4$ fm and clearly mimics here the confinement part of $\alpha_{qq}(r)$. This is also apparent in quenched QCD [@Kaczmarek:2004gv]. Remnants of the confinement part of the QCD force may survive the deconfinement transition and could play an important role for the discussion of non-perturbative aspects of quark anti-quark interactions at temperatures moderately above $T_c$ [@Shuryak:2004tx; @Brown:2004qi]. A clear separation of the different effects usually described by the concept of color screening ($T\;\gsim\;T_c$) and effects usually described by the concept of string-breaking ($T\;\lsim\;T_c$) is 