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Sorry, I highly doubt a CO2 increase from 0.03% to 0.04% will result in a 5°C or more warming, that's just unrealistic.
By that logic, certain periods in Earth's history when there was much more in the atmosphere, for example the Jurassic with 0.20% would've been >85°C hotter, which we know is bullshit
Even with a super logarithmic curve, you can't bend and stretch things that far
And what's often missing is the buffer effect, higher CO2 also means higher carbon assimilation by the flora, this may be delayed but eventually we'll see the effect