That wouldn't help at all. When the Stage 3 engines ignites, the Stage 2 is disconnected by explosive bolts and all power lines are severed. The Stage 2 remains pretty much inert after that, only venting the tanks.
Looks more like multiple cable bundles getting connected. its not really parallel and it has the same appearance as cables somewhere else. A better picture could help there, especially since we only see one third of the interstage there.
Would be a bit weird to put an radiator into the place without any airflow during launch. And you can use the structure of the rocket as heat sink.