No,
peterc005, the science is not "well established". Nothing like it. Not even close.
I have been following this issue since the late 90's and can tell you that there is considerable scientific opinion favouring the skeptical side of the debate.
In fact, I believe there are more skeptical scientists than there are believers. I have no proof of this, but this is just my observation.
Heard of the Oregon Petition? That is a list of over 30,000 scientists who dispute the idea that man's CO2 emissions are having any dangerous effect on the climate.
Over 9,000 on that list have a PhD. Here are the disciplines from which that 30,000 odd is comprised:
Atmospheric, Environmental and Earth sciences: 3,805 (Climatology: 39)
Computer and Mathematical sciences: 935
Physics & Aerospace sciences: 5,812
Chemistry: 4,822
Biochemistry, Biology, and Agriculture: 2,965
Medicine: 3,046
Engineering and General Science: 10,102
https://en.wikipedia.org/wiki/Oregon_Petition