I don't believe the spring should be getting hot, as the current is carried by the wire running in the center of that plunger assembly. I'm guessing that your problematic plunger assembly has a bad center wire, forcing the current to flow through the spring. I don't know why Classicparts lists it as 6 volt only. Jim Carter doesn't make that distinction on the very same part. If there were a difference between a 6 volt and 12 volt plunger, I would think that a 6 volt plunger would have a heavier gauge center wire and work just fine on 12 volts. My assumption is based on the difference in 6 volt vs 12 volt wiring harnesses and battery cables. 6 volt wires are larger in diameter.
Carl