Not likely, since the intervening material probably lets most of the radio emission through. So the radiative coupling between the synchrotron emission and that material is too weak to raise the temperature by much (if any).

> There's got to be some dust out there that's over the hagedorn temperature.

Interstellar dust grains are thought to be destroyed at temperatures of 1500-2000 K (depending on composition). And their absorption cross-section for absorbing radio waves is fairly small.