I just don't let a round cook for more than a few seconds, typically. Powder being a cellulose product, it's a decent insulator, so doesn't change super fast. I think that's why I don't see tune change so much, if any, due to bbl temp but rather, ambient, as the powder has time to change.
You and others have touched on station pressure as well as temps so I'll add what I've been able to observe a bit.
First thing is, smokeless powder turning from a solid into a gas is a chemical reaction and all chemical reactions are temp dependent.
The other thing is that air pressure very much appears to have an offsetting affect on tune as opposed to temp. Which very well may explain why identical temp changes from day to day...one day the tune clearly goes away but the next, it seems to hold tune very well. Pressure and temp are related but they don't always change linearly and the same from day to day, for example. I've seen this both ways many times but the first was in tornadic conditions where temp was stable but tune left, badly and I struggled to find it moving the tuner the way I "thought" based on temp and group shapes. Something to keep in mind is all. But the key to keeping a gun in tune is generally group shape. I can't emphasize that enough. Shooting in a tornado or a hurricane, where the air pressure just plummets, does seem to change the direction you would need to go, be it tuner, seating or powder, though. I've tested this three times and it seemed to hold true. Tough conditions to replicate, fortunately.
