You should read the section on gas safety before attempting any repairs.

The Klixon valve is a gas safety device designed to shut off the flow of propane if the burner flame goes out. Because the assemblies that use the Klixon valve are usually very old, there seems to be a high tendency for the various fitting on the assembly to leak. It would be a good idea to wet the assembly with a soapy solution before and during your testing of the valve.

The Klixon consists of a bi-metallic disc that is concave at normal temperatures. In this position, the valve connected to the disc is held in a closed position, preventing the flow of gas. (Above) When lighting the burner, an external lighting flame is applied to the housing containing the bi-metallic disc. If no other lighting mechanism is present, a small wick-like cloth soaked in kerosene is a good external lighting flame. When sufficient heat is transferred to the bi-metallic disc from the lighting flame, the disc snaps into a convex position, with an audible click, and opens the valve allowing the flow of propane through to the burner. (Below) The lighting flame then ignites the burner flame. A soft aluminum tongue, which is also rolled around the disc housing, is in contact with the burner flame and provides enough heat to the disc to keep the valve open.

If the burner flame goes out, the tongue cools and therefore the bi-metallic disc cools, causing it to snap into the concave position, with an audible click, and close the valve. (Above).

The bi-metallic disc of the Klixon should make an audible snap when opening and closing. If it doesn't make the noise, it's not working right. In its prime, the Klixon valve was declared "not repairable". If it was bad, you replaced it. The only exception was the aluminum tongue, which was replaceable. Today, the Klixon valve is obsolete and essentially impossible to get. If the aluminum tongue is broken off, you may attempt to jerryrig something to transfer heat to the bi-metallic disc. However, if the Klixon valve itself is bad, it's time to think about replacing your refrigerator. Although it's theoretically possible to convert the burner assembly to something else (including adding a safety valve and thermocouple), it's not really practical. Besides the cost involved, getting the correct BTU output is difficult.

Older Dometic refrigerators that used the Klixon valve also used ceramic burners. A ceramic burner consisted of an inner and outer stone. This ceramic stones are very fragile and also obsolete. Be very careful when even getting close to them.