I think that is the often interpreted conclusion, that a hot barrel causes the combusting charge to somehow burn hotter, and therefore raise pressure.
My conclusion is quite the opposite. That the relatively cold barrel quenches the burning charge REDUCING pressure. This is, and I think I'm correct in stating this, a law of thermodynamics. That if you cool a gas in a confined space, it will reduce in volume and therefore pressure. And a cooler barrel will quench the gas charge more than a hotter barrel. It is an indisputable fact that heat from the burning charge is being transferred to the barrel during ignition.
Shooters work with this effect by warming the barrel before shooting for record, and allowing as much cooling time between strings as necessary to keep the barrel within the best operating temperature range.
In the study I reference above, the barrel was not allowed to go above a certain temperature, so it would be interesting to see what happens if the barrel is allowed to continue to heat. Would the rate of pressure rise continue to rise proportionate to the barrel temp rise? Or would it plateau, and if so, at what temperature?
At some point you'd get cook-off of the round, but that is typically the primer detonating. What if the bullet is chambered and fired quickly, before primer cook-off can occur? Its burn qualities must be effected by temperature of the primer compound, in fact the author of the above study ends his paper by bringing up this very subject. Is it primer temperature, and not barrel temp that has the most effect on pressure rise?
Inquiring minds are sure to find the answer.