No he's 100% safe for now is my guess.
You either fire your coach immediatley afetr the season ends so you can have a new coach in place for the draft and shaping your team over the summer or you wait until during the season when a coaching change gains you maximum brownie points with fans etc.
You don't waste the chance to "balme" all the problems when your team has lost 10 of 12 games in Dec on the coach by firing him. You don't waste the chance to appease fans screaming for blood when your first round draft pick is grabbing 2 rpg or your "star" is moping on the bench with a hangnail. You want to be able to fire the coach and say hey look I did SOMETHING.
Will Frank survive the year? Probably will he be there the year after ..that's yet to be seen. As subs mentioned Carter will likley be gone. Jeffeson is gone and Kidd is gone. If he can get some performance out of this new group he's probaly due for an extension.