  We show that the Polyakov loop approaches its asymptotic value at high
temperatures {\it from below} in any strongly-coupled gauge theory at large
$N_c$ with a dual supergravity description. In these theories the Polyakov loop
can be used to define a quantity that behaves as a free energy of a heavy quark
in the medium. This should be compared to the recent lattice results in pure
glue SU(3) theory at high temperatures where the Polyakov loop approaches its
non-interacting limit {\it from above}. We show that the "heavy quark free
energy" obtained from the renormalized loop computed on the lattice does not
behave as a true thermodynamic free energy. We conjecture that this should
always be the case in asymptotically free gauge theories.
