Well, the Keeling Curve (the record of CO2 accumulation in the atmosphere since the late 1950s) shows pretty steady accumulation, though it's not quite a linear line, it's slightly exponential.
https://climate.nasa.gov/vital-signs/global-temperature/
If you compare that to the global temperature data presented in the same kind of graph, there's this relatively flat period from the 1950s through the 1970s, before the steady climb begins:
https://climate.nasa.gov/vital-signs/global-temperature/
CO2 is best understood as having its most potent effect at about ~12 km up in the atmosphere, this is where under pre-industrial conditions there was a large 'escape window' for infrared radiation (due to colder temps and lower pressures). That warming in turn drives water vapor feedback at lower levels in the atmosphere, with the water vapor accounting for 2/3 or so of the actual radiative trapping and the CO2 accounting for about 1/3 (then there's methane, a compounding factor but IIRC it's about 1/20th overall).
If we take the Milankovitch cycle of glacial ages into account, the world without fossil CO2 should have been steadily sliding into another ice age (with the warm peak about 10K years ago). So the flattening out period represents perhaps the end of that trend (driven by orbital parameters, and associated feedbacks w/ ice sheets and CO2).
Now the CO2, thanks to steady increase, is the dominant factor controlling global temperature trends, and the global temperature is basically just tracking the global atmospheric CO2, with a lag time of at least several decades (I think it's more like 100 years for the global temperature to catch up with the global atmospheric CO2, but that's a matter of debate).
Conclusion: even if we take dramatic action to curb fossil fuel use (which is a good idea), we're going to be stuck with a steadily rising global temperature for at least 100 years before leveling off (and this ignores issues like permafrost outgassing of additional CO2 and methane destabilization in shallow marine sediments). Hence humans are going to have to plan for adaptation to these new climatic conditions. The point has been well tipped, and we're in for it.