I hiked the teton crest around Sept 20 last year. First day was pretty cool, low 50s and very windy when we got off the tram. Rained a little bit, but warmed up as the day went on, probably 60s in the sun.
Night time temps were high-20s/low-30s. I brought an older sierra designs down bag and was generally OK.
We got rained/hailed on pretty hard the second day, but made for some awesome scenery with the fog that collected afterwards.
Third day was sunny and high 60s. Very comfortable.
The scenery was amazing. Ran into a bear along the trail and a moose at the end as we were coming out to the parking lot.
I'd say a 20 degree bag would be perfect. Bring hat+gloves, rain gear, puffy, and long underwear and you'll be fine.