You know, I don’t think history has been fair to Lord Kelvin on that. Of course he’s wrong, but you have to consider that he was mainly arguing against uniformitarians who were saying the world was infinitely old. Thermodynamics did show that they were wrong, and in a very real sense he was much closer to the real value than they were, just not in a way useful to geologists. I’d consider it more different experts talking past one another.
Science is settled that people don’t spontaneously mutate into dinosau – oh no! More likely, when someone starts their argument by explaining how nobody ever really knows anything, you can be assured they are about to try selling you a bill of goods. This spiel is no exception.
Right off the bat there is the fountain of money for researchers promoting climate change. There is some money given for researching climate, same as other important fields, but the feeding frenzy you describe is pure fiction. At the same time, there is so much money being pumped into think tanks trying disprove it, the only explanation they haven’t had more results is that the evidence is just against them. So this is a lie on par with swiftboating. Enough with it.
Your other particulars are full of mistakes too. There’s no complete geological correlation between carbon dioxide and temperatures because there are lots of other factors, but it certainly is there, as things like the much-cited Vostok cores support. There was no “warm” period during the Middle Ages comparable to what we have now; there was a warm period in Europe, but not for the globe. Computer models actually can help provide falsifiable evidence if you understand how to use them in combination with data. There has been a little contention over that data, but not on a scale that actually changes the results.
And most importantly, doubt per se is not the hallmark of real science. Scientists always look for evidence that might overturn things, but when that evidence is not forthcoming, they don’t invent doubt for its own sake. That’s rather the work of people trying escape what evidence shows, deniers and creationists, who are anything but true skeptics.
Edit: Welcome to the boards, by the way. You might have a better time on one of the plasma cosmology threads.