The link between atmospheric CO₂ and rising global temperatures cannot be dismissed as a case of “correlation and causality.” Wally Broecker’s Are we on the brink of a pronounced global warming?,
the first scientific paper to use the term “global warming,” appeared in 1975. As noted in
Happy 35th birthday, global warming!:

It is very instructive to see how Broecker arrived at his predictions back in 1975 – not least because even today, many lay people incorrectly assume that we attribute global warming to CO₂ basically because temperature and CO₂ levels have both gone up and thus correlate. Broecker came to his prediction at a time when CO₂ had been going up but temperatures had been going down for decades – but Broecker (like most other climate scientists at the time, and today) understood the basic physics of the issue.[My emphasis]

Also, as noted in A Response to Stephen Koonin’s Call to Inaction

One of the most widely held [misconceptions about climate science] is the idea that predictions of climate change rest solely on highly complex computer models.
This is far from the case; basic physics and very simple models all show that increasing greenhouse gas concentrations lead to nontrivial warming.
In 1906, the Swedish chemist Svante Arrhenius estimated that doubling CO₂ concentrations would increase average global surface temperature by around 4^oC;
his calculations were done with paper and pencil. If the computer had never been developed, climate science would still have identified the substantial
risk incurred by changing by hundreds of percent the concentrations of long-lived greenhouse gases.

This work of Arrhenius was also mentioned by Neil deGrasse Tyson in Cosmos earlier this year.

Also, as pointed out in Climate Change and Fragility Policy, uncertainty
about models works both ways:

What is missed by the discussion of “skepticism” is
that its impact on decisions should lead to increased,
not decreased conservatism in the presence of ruin. As
we show intuitively in Figure 6 and mathematically
in Appendix C, more skepticism about models implies
more uncertainty about the tails, which necessitates
more precaution about newly implemented techniques,
or larger size of exposures. Nature might not be smart,
but it has thinner left tail.

Mathematically, more uncertainty about models in-
creases the scale of the distribution, hence thickens the
“left tail” (as well as the “right one”) which raises the
potential ruin. The survival probability is reduced no
matter what takes place in the right tail. Hence skepticisim
about climate models should lead to more precautionary
policies.