  We discuss the temperature dependence of the screening lengths in quenched
and full QCD using the non-perturbative lattice approach. We analyze the
temperature dependence of distances which are defined as moments of quark
antiquark free energies. These distance scales are supposed to describe the
geometric size of partonic clouds which screen static charges in a medium and
characterize distances beyond which the quark antiquark free energy is to large
extent dominated by medium effects. At asymptotic high temperatures these
moments can be related to the inverse Debye mass. In our numeric analysis we
find that these moments drop rapidly in the vicinity of the phase transition
and indicate distances which are about twice as large as the inverse Debye mass
found in earlier studies. Our analysis supports recent findings that indicate
that $J/\psi$ will show significant medium modifications only at temperatures
well above $T_c$.
