  A comprehensive parameterization of the colour singlet heavy quark free
energy above $T_c$ is given, using the lattice data in quenched ($N_f=0$) and
unquenched ($N_f=2$ and $N_f=3$) QCD. The corresponding (temperature dependent)
potentials thus obtained are then inserted into the Schr\"odinger equation for
the charmonium and the bottomonium in the deconfined phase of QCD. The solution
of the equation provides an estimate of the melting temperature and of the
radii for the different $c\bar{c}$ and $b\bar{b}$ bound states.
