  Applying the AdS/CFT correspondence, the expansion of the heavy-quark
potential of the ${\cal N}$ supersymmetric Yang-Mills theory at large $N_c$ is
carried out to the sub-leading term in the large 't Hooft coupling at nonzero
temperatures. The strong coupling corresponds to the semi-classical expansion
of the string-sigma model, the gravity dual of the Wilson loop operator, with
the sub-leading term expressed in terms of functional determinants of
fluctuations. The contributions of these determinants are evaluated
numerically.
