Normally true, but this is a special case
The flue itself will be a stovepipe, and the actual fire does not get very hot -the rocks will never reach the 900 degrees necessary to burn lime. The fire for cooking cheese has to be very slow and controlled, and nearly all of its heat will go directly into the copper vat (this is the chief advantage of using copper)
In fact, in the Swiss Alps traditionally the cheese making huts are highly sealed, more so than any other building, because all heat needs to be retained for the cheese.
And furthermore, I will probably give the inside a thorough coating of mud with wood ash mixed in to serve as both a fire shield and to bring the casing itself to near proximity with the vat -almost touching. The vat has bulging sides, allowing it to fit snugly into such a box and retain as much heat as possible.