I see, it's not that easy as it looks like. Let's make it a bit more complicated.
I guess the important part is the meaning of "they heal that amount of damage". Does that mean the damage the would suffer from the burning condition without modification (burning 2 means 2 damage) or the damage after applying any prevention (burning 2 + armor 1 means 1 damage)?
What about the first sentence from the Rail Golem as well as the upgrade. They do not suffer damage from the Burning Condition. Since the upgrade on it's own says the do not suffer damage, they can not heal any damage. Instead is the keyword. That's why it could mean that do heal the wounds equal to the burning value. On the other hand, wouldn't they write the "heal wounds equal to the burning condition"?
In our last games we decided that it won't work. Otherwise my Rail Golem would heal about 5 to 9 wounds each round, thanks to the Captain! sounds a bit broken...