Look at this plot of Global Mean Surface Temperature (GMST) and atmospheric CO₂ over the last 450 million years.

You’ll see it clear as day: periods where CO₂ shoots UP while temperatures drop. Other times CO₂ rises and temps rise too.  - Dr. Matthew M. Wielicki@MatthewWielicki
The relationship is all over the place. 

• This is pretty much conclusive evidence that Earth’s surface temperature is remarkably insensitive to CO₂ changes. 
• If CO₂ was the dominant driver, we’d expect tight, consistent coupling — not this messy decoupling over deep time...