Temporal transporters are an advancement on transporter technology, allowing the user to transport to a desired space and time.
Wells-class timeships are equipped with temporal transporters, one is even located at the starboard-aft of their bridge. The transporter is used in unison with several other technologies, such as temporal sensors and temporal shields. Temporal sensors allow for the precise moment and location for the transport to occur, and temporal shields are raised before making any temporal transports. Presumably, this is so that if the agent sent back in time alters the timeline, the ship is not affected (for example, being erased from history, or never existing in the first place.)
When the USS Relativity-G needed to stop a temporal disruptor from destroying the USS Voyager in 2375, they used their temporal transporter to beam back and retrieve Seven of Nine moments before the ship exploded (so that no one would notice she was gone.) On the Relativity, a display shows a point reaching a line on a TCARS display - this is the transporter pattern reaching the "temporal threshold" to reach the 29th century.
After bring Seven back several times, they surmised the place and time the bomb was placed (and even caught the saboteur) but then they needed to stop him when it first happened. After beaming Seven back again, she succumbed to Temporal psychosis, a psychological effect of using the transporter several times, that leaves the user mentally unstable, or even dead. (VOY: "Relativity")
Background
- It seems the transport is awfully dangerous to be used routinely on missions, one theory is that it develops when the transporter is used repetitively by a person over a short period of time.
- Wells-class timeships as well as the Aeon shuttle were able to move the entire ship through time, which may explain why so few people actually suffered from Temporal psychosis.
- It's likely that the "Time portals" used by Daniels and the temporal agents of the 31st century are advancements on this technology.