(covers information from several alternate timelines)
A temporal core was a central component of some vessels which possessed time travel capabilities.
29th century Federation timeships possessed temporal cores, which had to reach cascade potential before the generation of a temporal rift. In 1996, 20th century industrialist Henry Starling attempted to use the timeship Aeon to create a rift to the future, a process which required him to initiate a temporal inversion, upon which the temporal core was able to generate the rift. (VOY: "Future's End, Part II")
The weapon ship invented by Krenim scientist Annorax was powered by a temporal core, which kept the vessel out of phase with normal spacetime, thereby protecting it from the changes to the timeline which it initiated. In 2374, Captain Janeway piloted the USS Voyager on a collision course with the weapon ship in a last-ditch effort to defeat Annorax. Upon the collision, the weapon ship's temporal core destabilized, initiating a temporal incursion within the ship itself, erasing it and all of its temporal incursions from history. (VOY: "Year of Hell, Part II")