It happens in fall specifically because it's not a good season for raising chicks in nature. Even in warm zones there's a decrease in food availability as the plants are not fruiting, so even the bugs are less. Some trees are changing out their leaves so the protective cover is diminished. And the predators are getting hungrier.
For those reasons, they don't need to lay eggs in fall and that leaves available nutrients they can use to make new feathers.
As others have said, chickens are naturally warm region birds. The replacement feathers are no different, unlike mammals which change coat types. So, I think it doesn't have anything to do with temperatures, only when they can afford to make feathers.
Spring: Eat up to recondition, find partner, build nest, Lay Eggs.
Summer: Feed chicks, feed chicks, feed chicks.
Fall: Make Feathers, try to fatten up.
Winter: Search continually for enough food to get by.
For those reasons, they don't need to lay eggs in fall and that leaves available nutrients they can use to make new feathers.
As others have said, chickens are naturally warm region birds. The replacement feathers are no different, unlike mammals which change coat types. So, I think it doesn't have anything to do with temperatures, only when they can afford to make feathers.
Spring: Eat up to recondition, find partner, build nest, Lay Eggs.
Summer: Feed chicks, feed chicks, feed chicks.
Fall: Make Feathers, try to fatten up.
Winter: Search continually for enough food to get by.