Don't worry for downvotes. I downvote everything I disagree. How else would you know it? I am also frequently downvoted, and I find some pride in that.

But go back to the topic! You say it's possible that despite of the fact that T(y)<T(y-20), where CO2(y)>CO2(y-20) - the function still grows? Uhm ... I am not that certain. It is at least bumpy.

sensitivity of 3 degrees to CO2 doubling

This I find particularly fishy. Half the amount of CO2 10 times! Then it will be less than 1ppm CO2 in the atmosphere. Do you expect 30 degrees cooling?

I doubt it.

But do half it 40 times. Some molecules of CO2 are still with us. Do you expect 120 degrees cooler outside?