It's pretty hard to measure temperature.  Even with the most modern readings, because most of the earth is water, and we cant measure the deep ocean.  The Argo network is under funded.  Satellite data from the polls can vary.  That's even with modern space technology.  Before that we had proxy methods such as tree rings and ice cores which are even more sketcy.  

But you can safely say that CO2 is a greenhouse gas, that traps heat.  And since energy cant be created of destroyed acc. to the well-tested 2nd law of thermodynamics, you can assume that the heat goes somewhere.  And that C02 has a log effect on temperature, with possible feedback mechanisms, mainly water vapour.

Figuring out temperature involves a lot more detective work that people realize.  And scientists dont want to admit that, because it's red meat for the skeptics.  Then there is the sensationalism in the media which doesnt help.

We probably have warmed about 1.5C in 150 years and c02 probably is a greenhouse gas that traps heat, on land, but in also some strange cycles in the ocean.  There is an awful lot of detective work that is needed to come to that conclusion, but it's prolly just about right.

Whether this is catestrophic is anyone's guess.  Probably not, but those wanting to be cautious have a point.  Using it as a tax strategy is non-sensical, tho.  If humans were able to solve simple problems, climate change might be a good one to tackle.  But we are barely able to stop ourselves nuking each other, in which case we'll need all the heat we can get.  Maybe we'll get smarter when the machines help us think for ourselves...