That's definitely true about hunting the dogs in warmer temps, but you need to remember this. Chickens are notoriously hard to hunt over pointing dogs later in the year. The cover thins out and they can see you coming from a long way away. Trying to get a point, or even close enough to shoot a bumped bird will be VERY frustrating in November.
Pass-shooting while they are en route to feed fields is the traditional method of hunting chickens in Kansas. The season used to open the weekend before pheasant season and there wasn't an early season. I still remember the Wichita Eagle's article about the "new" early season for chickens for people who wanted to hunt them over pointing dogs.
That early season is open until October 15. If you're serious about shooting one over a point, I wouldn't wait an longer than that. It's just too hard to get close enough in the later season.