The T-Infinity Temporal Terminator is created by Skynet. Its purpose is to make sure the timelines don't get out of balance. By far, it seems there is only one prototype created by Skynet and sent to "correct" the timeline.
The T-Infinity is built with an onboard time displacement equipment, making it possible to relocate itself in time. It is able to trans-locate direct hits from a weapon and not be destroyed. However, an indirect hit does weaken it. 
Terminator 2: Infinity
Skynet somehow found out the timeline is unbalanced when Uncle Bob appears in the same date, and decides to correct it by using a T-Infinity. The T-Infinity is sent back to July 17, 2009 just before John Connor becomes the leader of the Resistance.
Skynet dispatch the T-Infinity again from 2033 to 2015 in order to kill Tara Connor. During a raid in the Resistance Headquarters, the T-Infinity is temporally disabled by John Connor with EMP pulse and a steel bar, causing its onboard time displacement equipment to malfunction. Thus, both John Connor and the T-Infinity are sent back to Alabama in the year 1996.
The T-Infinity arrives Birmingham, Alabama in 1996. The malfunction has caused a confusion within its system, thus its mission priority becomes Sarah Connor.
The machine goes to young John Connor's school and kills the principal, waiting for Sarah Connor. It fails to terminate Sarah upon the first encounter. T-850. The T-Infinity follows her to the street and begins to fight the T-850s.Sarah runs to the street, only to face the army of the
After destroying the T-850s, the T-Infinity uses the chrono-imager to track down Connors to their hideout in the woods, only to be confronted by the Connors. During the battle, the machine's right arm is destroyed by John Connor with a bazooka. The machine is later destroyed by a Dire Wolf, a wolf Terminator used to destroy the T-Infinity. After destroying the Dire Wolf, John Connor uses the onboard time displacement equipment from the remains of the T-Infinity to travel back to the 2015 with Kyle Reese. Soon after the arrival, John uses T-Infinity's neural network to set a coordinate for a missile to hit the Skynet Hub in Nebraska, destroying Skynet once and for all.
- Terminator: Infinity
- Terminator: Revolution