The Temperature Dependence of the QCD Running Coupling
  We study the running of the QCD coupling with the momentum squared ($Q^2$) and the temperature scales in the high temperature limit ($T > T_{c}$), using a mass dependent renormalization scheme to build the Renormalization Group Equations. The approach used guaranty gauge invariance, through the use of the Hard Thermal Loop approximation, and independence of the vertex chosen to renormalize the coupling. In general, the dependence of the coupling with the temperature is not logarithmical, although in the region $Q^2 \sim T^2$ the logarithm approximation is reasonable. Finally, as known from Debye screening, color charge is screened in the coupling. The number of flavors, however, is anti-screened. 
F. M. Steffens