By its very nature, the Temporal Cold War isn't limited to one era. The "front" of the TCW being fought in the 2150s was resolved in 2154, but we know it has other battle fronts being waged in other historical eras, past and future, and that its participants came from many different eras in the past and future. From the perspective of linear time, it's impossible to say the TCW is ever permanently "over," at least until you reach the end of the "front" that's furthest in the future -- and the furthest one we know of is in the 31st century. So there's always the possibility of the TCW being revisited, if not in ENT then in other series.
In fact, fittingly, one can make a case that it was "revisited" before it was even created. In a DC Comics TOS story written a decade before ENT premiered, Howard Weinstein brought back Gary Seven and revealed that he was a member of the Aegis, an organization dedicated to protecting history from other time-travelling factions that sought to change it. This was no doubt based on Roddenberry's original premise for "Assignment: Earth" as a standalone series, but Howie's description of the Aegis (built on by Greg Cox in his Gary Seven books) can fit perfectly into the Temporal Cold War concept.