Hi, I am not familiar with your coach so not sure what the specific purpose of that relay (solenoid) actually is. Generally a relay allows higher current devices (like loads such as fans, lights etc) to be controlled by lower current devices (like switches). So on a basic 4 wire relay the operating coil winding is connected to the switch (low current device) and the heavy current loads being controlled are connected to the large relay load contacts. See attached simple diagram.
It “sounds” like you are saying the coil measures 12vdc across its terminals always and it feels very hot. If this relay has operated and closed its load contacts, there should be zero volts measured across those closed heavy load contacts......if those contacts are making good contact with each other and if they are both in good electrical conductive condition. If the heavy load contacts are in poor electrically conductive condition then they can form a resistance to current flow and can get hot when high currents try to pass through them.
So it might be worth investigating if its the coil winding or poor load contacts causing the high heating. If you are not comfortable testing the relay you could either replace it with a correct OEM unit or have an RV tech check things out.
If this relay coil is quite hot it may be a sign of shorted windings in the coil (this usually prevents proper operation of the relay though) or it might be normal if it is a relay designed for continuous duty (meant to be powered over longer time periods). Perhaps someone who owns a similar coach will advise on their similar relay; what it does and how hot it gets when powered.
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