Usually compressed gasses expanding through a valve make the valve cold not hot (PV=nRT) If the pressure drops the temperature also has to drop. Seems strange and worth investigating.
The solenoid is an electromagnet. There is a coil of wire that forms a magnetic field that pulls the valve open. That will generate heat as well as a magnetic field. When you are done cooking turn off the solenoid, it is draining your battery.
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