From 
Jay Cutler Split Stats, here are his splits by quarter for the 2008 season:
1st Qtr 94/143 (65.7%) for 1056 yards (7.39 ypa), 7 TDs, 5 interceptions, 1.0 sacks, 89.4 QB rating
2nd Qtr 91/146 (62.3%) for 1103 yards (7.56 ypa), 5 TDs, 4 interceptions, 2.0 sacks, 85.5 QB rating
3rd Qtr 99/160 (61.9%) for 1155 yards (7.22 ypa), 2 TDs, 5 interceptions, 3.0 sacks, 74.9 QB rating
4th Qtr 100/167 (59.9%) for 1212 yards (7.26 ypa), 11 TDs, 4 interceptions, 5.0 sacks, 94.2 QB rating
Looks like he was at his best in the 4th quarter.
In looking over these splits, I noticed on passes thrown 31+ yards downfield, he was only 4/27 for 193 yards, with 1 TD and 4 interceptions.  I was surprised to see this, given the quality of his WRs and the reputation of his arm... at some point, they should have just stopped throwing downfield...