Heavy Quarkonia at High Temperature

We present a new method to study the properties of heavy quarks at finite temperature. It combines non-relativistic QCD with an improved gluonic action on anisotropic lattices. The efficiency of the approach is demonstrated by the first non-perturbative calculation of the temperature dependence of low-lying quarkonium "pole" masses. For ground state meson masses in the region between charmonium and bottomonium we find only very little variation up to our highest temperature which corresponds to T approximately 1.2 Tc while first excited states indicate a large mass shift.