I am familiar with hypothetical studies like this one.
if you read very far into the article, you understand the basis.
Now let's discuss the possibilities of say a 3°C " increase from what they were before the Industrial Revolution."
The discussion starts with, how is the pre industrial temperature defined?
Most use the average instrument record before 1900.
The IPCC says that by 2020 the average temperature was 1.07°C above the preindustrial level.
Of that 1.07°C, in the modified HadCrut5 data set 0.31°C was pre 1950 warming considered natural.
So we have 0.76°C of warming from unknown sources, While the
NOAA AGGI says the index increased from 280 ppm
to 504 ppm. That alone would tell us that the climate's sensitivity to added CO2 would be,
0.76°C/ ln (504/280)=1.2929. so 1.2929 X ln(2) = 0.89°C.
But it is not that simple, the climate has a 10 year lag between emissions and maximum warming, so we have to evaluate
the 1.07°C based on emissions up to 2010, less any forcing warming between 2010 and 2020.
In 2010 the AGGI was 469 ppm, so the forcing warming between 2010 and 2020 is 5.35 X ln(504/469) X .3=0.115°C,
This would make the sensitivity 1.07°C - 0.115°C= 0.955°C/ln(460/280)= 1.9237, so 1.9237 X ln(2)=1.33°C.
Under a climate sensitivity of the high end of what we have observed so far, CO2 levels would need to be at ~1330 ppm
to achieve warming of 3°C above the pre industrial level.
To put this in perspective, that is 884 ppm above where we are now, and it has taken us 140 years of unregulated
CO2 emissions to increase the level by 136 ppm.