The Temporal Cold War was a protracted struggle involving several factions of time travelers, which had effects from the 20th through the 31st centuries.
The 22nd century combatants included the Suliban Cabal, as well as the United Earth Starfleet. Participants from later centuries include the Sphere Builders (26th century), the Order of Omega from the 28th century led by "Jamran Harnoth", the Na'kuhl from the 29th century and the United Federation of Planets (in both the 29th century and 31st century) as upholders of the Temporal Accord (which effectively protected the Federation's individual history). (DTI novel: Watching the Clock)
Shortly after the launch of the Enterprise by the United Earth Starfleet in 2151, the ship - and hence Starfleet - became involved in the conflict, fighting against the efforts of the Suliban, especially those of Silik, a prominent Suliban. (ENT episode: "Broken Bow")
The Enterprise would continue to play a role, helping to stop unknown forces from the future from tampering with 22nd century history. Crewman Daniels, a representative of the 31st century, enlisted Captain Jonathan Archer's help in stopping the Suliban Cabal. Later Enterprise helped stop the Na'kuhl from even starting the Temporal Cold War. (ENT episode: "Storm Front")