Heavy quark potentials are investigated at high temperatures. The temperatu
re range covered by the analysis extends from T values just below the decon
finement temperature up to about 4T(c) in the deconfined phase. We simulate
d the pure gauge sector of QCD on lattices with temporal extents of 4, 6, a
nd 8, with spatial volumes of 32(3). On the smallest lattice a tree level i
mproved action was employed, while in the other two cases the standard Wils
on action was used. Below T-c we find a temperature-dependent logarithmic t
erm contributing to the confinement potential, and observe a string tension
which decreases with rising temperature but retains a finite value at the
deconfinement transition. Above T-c the potential is Debye screened; howeve
r, simple perturbative predictions do not apply.