It doesn't actually take a lot of time. I start soaking the ammo when I get to the range, and fire it before I leave. The test only takes 15 min. to run, and that is because you're waiting a minute between each shot. People spend more time searching for temperature variation data on the net than it takes to run the test and it may be different for their load.
I don't shoot the ammo at a target when running the test, and you don't get that large of a temperature variation when shooting. But, it isn't as simple as a change in velocity. When the velocity changes due to temperature, it's no different that when you change the charge weight at one temperature. If velocity changes, pressure also changes (it must), so does barrel time (they are interdependent). So, the load gets re-tuned the same way it does when you vary the charge weight when working up a load. The POI changes not just from velocity change, but also from the barrel harmonics, the same way it would if you ran a ladder test.
Temperature stability is also important to maintain the precision of a load, not just for simplifying external ballistics.