It was somewhat ironic, but for a Time War, neither side used time travel in their offenses that much.
Using it as a defensive measure was almost expected, of course- ships jumping away from battle when they sustained serious damage only to return once they'd undergone the necessary repairs- but it had been almost an unspoken rule in the conflict that neither side would attempt to pre-empt any attacks or transmit warnings into the past about future assaults. Despite the Daleks' dreams of universal conquest, even they acknowledged that the Web of Time could only take so much before it was pushed beyond its limits, and the Time Lords' adherence to the Web of Time went without saying.
However, that didn't mean that there weren't areas of conflict where time travel was more than just a means of transport. While doing some research on potential areas of conflict around Earth, the man who had been known as the Doctor had discovered a particularly potent potential timeline dated around the later twentieth and early twenty-first century, the result of a rather fascinating time loop where a chain of events came into existence because it existed.
Apparently, in this pocket timeline, an artificial intelligence known as 'Skynet' was developed to take control of America's military defences, only for Skynet to decide that humans were the enemy and trigger a nuclear war to eliminate the threat. However, humanity had managed to rally in opposition of Skynet led by a man named John Connor, and when Skynet's defeat seemed certain, they had attempted to ensure their victory by going back in time to kill John's mother and John himself before they could become a threat, among other attacks.
The time-travel had been the real clue that the soldier needed; ever since that mess with Reginald Style's peace conference and the Daleks' near-conquest of Earth, he had been fully aware of the possibilities that alternate timelines could create themselves, and Skynet was too significant an anomaly for it to have arisen without some kind of interference.
It had been tricky to determine where he should act, but after travelling back and forth along the timeline, he had eventually managed to determine the precise location to travel to if he wanted to avert Skynet's creation. After examining a few components from the Terminators that Skynet had sent back, he had managed to confirm that there was no trace of non-Earth technology in their design, leaving him free to track down the first moment when Skynet's history contradicted the history he knew and take it from there.
Studying the large ball of energy as it appeared in front of him, the old man had to admit that it was a rather effective means of time travel given the resources available to the future it had come from. This particular bit of time-travel might have created a fundamentally unstable timeline isolated from most of the multiverse due to its paradoxical nature, but the Terminators alone could be a serious threat if the Daleks were 'lucky' enough to learn about them, so it was best to nip these events in the bud sooner rather than later.
As the Terminator materialised in front of him- that living tissue over its endo-skeleton was disturbingly realistic- the old man simply waited for it to stand up before he raised his gun and fired the energy blast directly at the Terminator's head, destroying the skull and the control chip in one shot.
Taking a moment to wait as the Terminator fell over to make sure that it wasn't a model capable of walking around without its head, the old soldier than walked up to the body, dousing it in thermite before he set it on fire. The remains would probably arouse some questions later on, but nobody would have any reason to think that they were anything more than some kind of accident, and even that interest would die down once it was confirmed that nobody had been hurt.
With the Terminator dealt with, that particular paradoxical timeline should be left in a satisfying dead-end. Without access to the Terminator's remains, Cyberdyne would never manage to complete the microchip that allowed them to perfect the Skynet project, and therefore the Terminators would never come into existence in the first place, or at least it would take far longer to develop the program and additional security protocols would be installed to prevent it triggering that nuclear apocalypse by the time it was brought online.
There was the issue of that 'Kyle Reese' fellow who'd been sent back to oppose the Terminator, of course, of course, but the soldier was less concerned about that. From everything he'd read of the war against Skynet, Lieutenant Reese was smart enough that he wouldn't do anything to attract attention to himself unless he absolutely had to, which meant that he should be content to start out by making a discreet observation of Sarah Connor and waiting for any sign of the Terminator. Even if he initially assumed that he'd simply arrived before it, eventually Kyle would realise that the Terminator wasn't coming, allowing him to accept his new life and move on to find something else he could do with himself in this era.
Maybe Reese would end up with Sarah Connor in the end, or maybe he'd move on; what mattered to the soldier was that Skynet had been eliminated for good.
Compared to what could have been, the questionable fate of one time-displaced soldier was an acceptable compromise (Particularly since, unlike Klein, he would have no desire to recreate the world he'd come from)…
AN 2: To those who haven't heard the audios, Elizabeth Klein was a companion/adversary of the Seventh Doctor; she originated from a timeline where the Nazis won the Second World War after analysing technology taken from Ace's backpack when the TARDIS landed in Colditz in 1944, but the Doctor of the new timeline was able to trick Klein into going back in time to try and 'capture' his previous self and thus give him all the information he needed to avert her history (She then went on to steal the TARDIS and try and rebuild her world despite the Doctor offering her a chance at reformation by travelling with him, but that's another story).