We see an evolution of the Terminator throughout Terminator 2: Judgment Day. He develops from a machine programmed to protect John to something more humanized. Although still a cyborg; he is able to adapt to his surroundings so he can fit in better with an all-human society.
We witness part of this development when John tells the Machine how to speak with a more colourful vocabulary.
There are also other moments where we get a glimpse of the Terminator becoming more self-aware of how he feels (e.g. When he smirks at John after picking up the Gatling Gun; when he explains to John the an understanding of why humans cry; to the final thumbs up he gives John as he's lowered into the vat of molten steel). Wow...even thinking about that scene still gives me chill-bumps :)
Anyway, as much as I loved these scenes, I can't help but wonder if the Terminator could have eventually started to feel negative emotions towards John. Emotions that would have eventually made the Machine either "feel" annoyed or angry.
Obviously, there's no code we can look at to determine if this could happen; but is there any evidence in the Terminator Universe that would draw the conclusion that the Terminator in T2 could have gotten angry at John?
Assume that it's with his existing programming; no virus or upgrades.