So what sort of temperature range are you testing? It sounds like you are heating/cooling the ammunition, and not the test barrel.
Last time I did it, I did 140F down to -20F. The high top temp was to simulate solar heating of a black rifle in the sun. I figured below -20, I'm not hunting.
I only forced the ammo temp, not the rifle. The rounds were quickly moved to the rifle and fired, and I'm comfortable that rounds ignited with the powder temp very close to the target temp. My working assumption is that powder (and maybe primer?) temp is all that matters, and barrel/action temp is irrelevant. In my experiences hot chamber/barrel caused by long strings of fire don't seem to increase velocity unless rounds sit in the chamber for a while which appears to support the "ammo only" approach as long as you hustle.
Plus I've got no hope of borrowing a thermal chamber that will hold a rifle fun as it would be.
