(covers information from an alternate timeline)
The Temporal War began when a rogue time-traveling faction, the Na'kuhl, returned to the 29th century after making several changes to Earth's history. With this egregious violation of the Temporal Accord, all the time-traveling factions began attempting to wipe out the others from existence. As a result, an already-existing Cold War escalated into a full-scale conflict.
This war was averted when Enterprise NX-01 destroyed the temporal conduit the Na'kuhl attempted to use to return to the future, restoring history back to its normal track. With full-scale war prevented, Daniels promised Captain Jonathan Archer that the Temporal Cold War would soon come to an end. (ENT: "Storm Front", "Storm Front, Part II")