After yesterday's rain and bad light affected affair, Durham resumed on 403-7 and lost Thorp who was stumped by Tim Ambrose, then had Ian Blackwell who had taken his total onto 158 bowled by Boyd Rankine.
Jeetan Patel took the final wicket, when former England international Steve Harmison was caught by Ian Bell to leave Durham all out for 433.
Ian Westwood was out early but a partnership between Tony Frost and Ian Bell of 117 took the score on. Frost was caught for 56 and with the score on 168, Bell was also caught, having made 76.
Jon Trott made 25, Jim Troughton 16 and Tim Ambrose ten before Neil Carter was out for a duck and Warwicks on 212-7.
Woakes (24) and Patel (6) both lost their wicket to Harmison as Warwicks ended the day on 264-9, some 169 runs behind.
At Binley Road, Warwicks Second X1 made 394 in their first innings with Woecestershire all out for 243. With an hour left of play, Warwicks were 55-2 in their second innings.