Jon Trott and Chris Woakes carried on from their overnight scores. Trott made 184 not out and Woakes was 131 not out as Warwicks declared on 484-7.
Michael Carberry was in fine form for Hampshire, hitting an unbeaten 183 as the home side put on 262 for the first wicket and closed on 309-1.
Ian Westwood took the only wicket when he had Adams caught by Trott for 90.