(covers information from an alternate timeline)
The Temporal War began when a rogue time-traveling faction, the Na'kuhl, came to the 31st century and defeated Daniels' faction 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 the 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")