Gas will expand to fill all space available, therefor volume (in the way you are using it) of gas is a non-relavant factor. Mass of the gas (more accurately, the number of gas molecules) times temperature devided by volume of containment vessel yields pressure.
This is why pressure and temp are linear.
As to barrel temp vs pressure: Denton has done the experiments and shown us the data. He knows that of which he speaks.
