Just remember, Greenland was named so about 1000 years ago, when it was green. Was humanity responsible for that bit of warming?
It would be hard to understand if the world today were NOT somewhat warmer than it was in the depths of the last ice age. That's why we're not in an ice age now, isn't it? And projections for future temperature increases are just that: projections. They are based on statistical models and the models are constantly changing, being refined, as our data collection improves. The problem is that the ways we collect that data are so much improved within the last 20 - 30 years, with the advent of satellite weather monitoring, that much of the data we are trying to compare it to from prior times is unreliable. How can we know what kind of evolution the Greenland ice sheets have undergone in the last 10,000 years or so? Sure, there's ice core sampling, but that's like looking at an elephant through a microscope and trying to decipher its shape with only a handful of views. Possible? Perhaps, but it's unlikely you'll get it exactly right.
As you noted, it would be foolish in the extreme to deny the existence of global warming, just as it would be foolish to deny that the earth is round. The big question is how much of that warming is caused by man's actions? If it's a lot, then yes, we should be able to have a large impact by reducing our carbon footprint. If it's only a little, than any attempt we make to mitigate it will also be quite minor.