  By making use of the finite-temperature real-time static potential that was
introduced and computed to leading non-trivial order in Hard Thermal Loop
resummed perturbation theory in recent work, and solving numerically a
Schr\"odinger-type equation, we estimate the quarkonium (in practice,
bottomonium) contribution to the spectral function of the electromagnetic
current in hot QCD. The spectral function shows a single resonance peak which
becomes wider and then disappears as the temperature is increased beyond 450
MeV or so. This behaviour can be compared with recently attempted lattice
reconstructions of the same quantity, based on the ``maximum entropy method'',
which generically show several peaks. We also specify the dependence of our
results on the spatial momentum of the electromagnetic current, as well as on
the baryon chemical potential characterising the hot QCD plasma.
