  We present lattice studies of heavy quark potentials in the quenched
approximation of QCD at finite temperatures. Both, the color singlet and color
averaged potentials are calculated. While the potentials are well known at
large distances, we give a detailed analysis of their short distance behavior
(from 0.015 fm to 1 fm) near the critical temperature. At these distances we
expect that the T-dependent potentials go over into the zero temperature
potential. Indeed, we find evidences that the temperature influence gets
suppressed and the potentials starts to become a unique function of the
underlying distance scale. We use this feature to normalize the heavy quark
potentials at short distances and extract the free energy of the quark system
in a gluonic heat bath.
