That solenoid only gets voltage as you turn on key , and only long enough to open and let enough fuel in to start then as it starts it opens and closes to keep it idling.you can turn off LP remove four screws and work that solenoid
Out there is an o ring on shaft that may be bad
As you have it in your hand turn key switch on
You should feel it click that is the initial burst of fuel to start , after it starts the ecm sends voltage to that solenoid to keep it idling
The long one that screws in is high speed fuel solenoid it opens after the rpm rate increases
You may have a faulty vaporizer or the base below the mixer (carb) could be leaking
Internally if heat affects it I would 1- check the vaporizer and see if it is freezing up if so check coolant in radiator and lines to it as well as thermostat 2- look at the r p m sensor 3- look at any relays that are in line with said solenoid
It may be getting too much fuel instead of starving. The vaporizer turns the liquid into vapor as you know but if the vaporizer isn't getting enough heat then the engine will get liquid and not a burnable vapor which leads to the things listed above