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.