You start Campaign mode only being able to achieve Heat levels 1 and 2 (City Police). By defeating certain Blacklist Rivals, you can then achieve the higher Heat levels:

Heat level 3 (State Police): Defeat the Blacklist Rival #13.
Heat level 4 (Undercover State Troopers): Defeat the Blacklist Rival #9.
Heat level 5 (Federal Authorities): Defeat the Blacklist Rival #5.
Heat level 6 (Cross' Street Racin' Unit): Defeat the Blacklist Rival #1 (final level only).

After you beat the Rockport's Most Wanted level, Heat level 5 will then consist of both the Federal Authorities and Cross' Street Racin' Unit.