I think Griese will probably cool off slightly but I expect him to remain a strong #2 QB to possibly a weak #1 QB depending upon match-ups. His biggest knock has been a relatively high INT rate but honestly it's no higher than Grossman's INT rate and at least Griese is putting points on the board.
The Bears with Grossman as QB for 3 games averaged 253 yards, .6 offensive TD's, and 11 points per game.
The Bears with Griese as QB for 3 games average 349 yards, 2.6 offensive TD's, and 28 points per game.
The Bears D/ST scored 1 TD while Grossman was starting and 2 while Griese was starting so the 17 points per game difference is really only a 14.6 point per game difference. Also Griese has more passing attempts (123 to 89) so here's a different breakdown through 3 games
Grossman averaged 52.8% completion rate, 10.6 yards per completion, .3 passing TD's, and 2 INT's per game.
Griese is averaged a 61.5% completion rate, 11.7 yards per completion, 2.3 passing TD's, and 2 INT's per game.
Grossman may have played slightly tougher D's than Griese has faced, but it's not a huge factor. I don't think Griese is the long term solution but at least he gives the Bears an opportunity to win. I'm not overly confident when Griese drops back to pass, but I don't throw up in my mouth like I did every time Grossman dropped back. And for the record I picked up Griese as soon as I heard he was starting. He is my #2 behind Hasselbeck but he has been outperforming Matt consistently.