  This work reports on investigations of the effects on the evolution of
viscous hydrodynamics and on the flow coefficients of thermal dileptons,
originating from a temperature-dependent specific shear viscosity $\eta/s (T)$
at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider
(RHIC). We show that the elliptic flow of thermal dileptons can resolve the
magnitude of $\eta/s$ at the high temperatures, where partonic degrees of
freedom become relevant, whereas discriminating between different specific
functional forms will likely not be possible at RHIC using this observable.
