Archery seasons in Idaho for deer, bear and elk start at the end of Aug. Deer/elk archery go through the end of Sept (and then general seasons open after that) and bear season goes until the end of Oct. (any weapon).
To be honest, I don’t spend much time in Sept. specifically chasing deer (though I’ll certainly take one if it walks by) – my focus is on elk, and increasingly, bear. And yeah, it can be warm here in Sept, even at high altitude, but as soon as the nights start to cool off, the elk will start rutting, and then it’s ‘game on.’
Another upsiade to bowhunting in Sept. is that animals are usually never going to be far from a water source.
Then again, we can get a week in Sept. that looks like this (as we did last year):