The opening post provides a link that I read and it doesn't say what "HC4 global temperature change" is. I have never heard of it and it doesn't represent a global mean of land-ocean surface temperature.
What is it?
I did address the claim that all of the global mean surface temperature change since 1970 is natural. Most of the global mean surface temperature change since 1850 is anthropogenic. Most or all of the
global warming from the Maunder minimum (1645-1715) to 1750 was natural.
The Berkeley earth graph below of global mean surface (land-ocean) shows a 10-year moving average that doesn't look anything like your graph.
http://berkeleyearth.org/archive/2019-temperatures/
Since 1980, the overall trend is +0.19 °C/decade (+0.34 °F/decade) and has changed little during this period. By continuing this trend, we can make a rough guess of how the near-future climate may develop if the forces driving global warming continue at their present rate.