I disagree with Mr Plod.
From the description you give, its the Thermostat and the torpedo shaped end clips into a bracket on the floor plate at the front of the heater, which is visible when only the front cover is removed.
View attachment 7640
The fact the thin copper tube has broken means the heater will not automatically regulate its heat output under thermostatic control. You cannot repair the copper pipe, as its content will have been lost. The copper tube does not carry gas, so there is not a gas leak concern, and you can continue to use the heater but you will need to adjust the flame manually
The thermostat works by having the torpedo sensing bulb and the capillary tube connected to a copper bellows inside the gas valve. the tube is filled with waxy oil that expands when its hot and contracts when its colder according to its returning room air at the base of the heater. When the room air is cooler the wax takes up less volume and the bellows in the gas valve contrats to open up the gas flow to the burner. as the room warms , the wax in th e bulb expands and opens up th e bellows in the valve which restricts the gas flow to the burner.
If the any of the parts of the bulb, capillary tube or bellows loses its containment, the wax stops working. Once broken the the system cannot be repaired, and the whole gas valve and thermostat has to be replaced, as its only supplied assembled, and calibrated.
For the safety of you and your family or other users of the caravan, the removal repair and replacement of the heater should only be carried out by an approved LPG gas fitter.
If it were the Thermocouple as Mr Plod suggests, the connection to the gas valve would be with a braided covered wire, and you could only see the end you describe as a "cigar" if the heater had been dismantled and the burner bar exposed.
PS its Truma not Truman