I suspect a third party would be far more likely to expect only one term and attempt to accomplish as much as possible without worry for re-election. Though there have been so few examples of "true" third party wins at high levels to know. The best example might be Jesse Ventura. As well, you might expect people who consistently run as a third party knowing no chance of winning to be less susceptible to the political machine than others.
Ventura only 'sought one term' because most of the state of Minnesota despised him and he never would've won re-election. He barely won the election as it was, with a bare plurality of votes in a 3 person race: http://en.wikipedia.org/wiki/Minnesota_gubernatorial_electio...
