There are two types of solenoids used (Actually 3) in the motor home's 12 volt system. (The third one is the starter solenoid, it is kind of a 2B. it is like #2 but designed only for short term engagement)
1: Latching.. On this type some kind of latch, generally a magnet, holds the contacts either open or closed, A much larger magnet (The Coil, is an electro-magnet) is strong enough to "FLip" the status of the contacts. This one should not get all that hot as it should not have power on it for more than one second. To flip the other way, Flip the magnet (Reverse the power flow).
2: Continous (2b: momentary see above) this type is normally open, closes when power is applied, spring opens when power removed, they run hot.
NOW: if it's running hot as in overly warm, not Hot as in "Live wire" ALL THE TIME, then one of two conditions exists.
One there is a charger source AND it is bi-directional (Shore power or engine power)
2: The Control circuit for it is shorted and feeding power to it when it should not. (most likely).
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times