  We determine finite temperature corrections to the heavy-quark (static)
potential as a function of the shear viscosity to entropy density ratio in a
strongly coupled, large-$N_c$ conformal field theory dual to five-dimensional
Gauss-Bonnet gravity. We find that these corrections are even smaller than
those predicted by perturbative QCD at distances relevant for small bound
states in a deconfined plasma. Obtaining the dominant temperature and viscosity
dependence of quarkonium binding energies will require a theory where conformal
invariance is broken in such a way that the free energy associated with a
single heavy quark is not just a pure entropy contribution.
