Should be fine.
You might have more luck asking people in the Small Form Factor forum as they obviously are running similar set ups in similar cases.
I think it's SimonMaltby though who I've seen running a 680 in a Shuttle, and I know there are a couple of people running 580s in TJ08e's, so it should be fine on the basis a 580 is hotter and bigger.
The 180mm Air Penetrator at the front of the TJ08 is a beefy fan and get's quite a bit of good airflow through the case.
kd