Be warned, I'm not a terribly social person, and my track record with understanding other folks' feelings hasn't necessarily been all that stellar in the past. That said, my thoughts on the subject are as follows:
I've noticed that a fair few contrarians--most or all of them, I'd say--ultimately base their objections not on scientific grounds, but on political grounds. There often seems to be, buried deep down under the rationalizations, unread literature, cherry-picked temperature records or intervals, and mis-cited quotes, a conviction that global warming isn't just a mistake on the part of the scientific community, like (technically) Newtonian physics or (in a few decades' time, perhaps) either String Theory or the Standard Model. Instead, it's typically viewed as a deliberate deception and an attack. Naturally, that point of view is going to instantly dredge up all the old "Us vs. Them" instincts, in which it doesn't matter which "tribe" is, logically and factually speaking, right about whether they have a claim to this or that territory. What matters is that the bad guys get defeated, because they're the bad guys.
So, ultimately, it's an emotional rather than logical battleground. I've read some articles by climate activists arguing that, therefore, the battle should be fought on emotional grounds. I don't know if that would work or not; maybe so. Like I said, social interaction isn't my forté. Personally, though, regardless of whether it worked or not I can't be comfortable with the idea. It feels far, far too much like manipulation, and even if it works (which, honestly, strikes me as kind of dubious. The contrarians have more experience with making emotional arguments, their audience tends to already identify with them politically and ideologically, and even if they could be won over by such means there's no Earthly reason why they couldn't be won back again--because ultimately, nothing has actually been learned) it doesn't produce people who understand the situation any better. They may happen to hold opinions which are more closely allied with the truth than their previous opinions, but their reasons for holding those views have nothing to do with physical reality and everything to do with their emotional state--and if their emotional state changes, Bizzam, so do their opinions.
So, on an individual scale at least, maybe it might be more productive to give both the emotional approach and the rebuttal approach the miss-in-baulk, and instead try to address the underlying problem, which will vary from person to person but is often a combination of simple ignorance (hardly a character flaw; it'd be very odd if most folks spent hours reading up on the minutiae of climate science, after all), a unfamiliarity with the many, many stumbling blocks that exist between oneself and even a partial understanding of the universe, and particularly a failure to realize their own fallibility, and to recognize that out of all the lies a person is told in their life, the most frequent, harmful, and insidious ones will be the lies they tell themselves.
...Says the not-terribly-social fellow with the admitted difficulty in parsing human behavior. I'd do well, I think, to heed my own advice about being aware of one's limitations...
