The Sun can't possibly explain global warming

Warmists allege CO2 must be the cause of the 0.7C global warming recovery from the end of the Little Ice Age in 1850, because they claim there isn't any other plausible explanation. 

The Sun and solar amplification mechanisms are dismissed as a cause because sunspots peaked around 1960, even though sunspots remained at relatively high levels, considered as the solar grand maximum of the late 20th century. 

Sunspot numbers and trend

The accumulated solar energy [sunspot time-integral] continued to increase until the end of the 20th century along with global temperature, and then both started to decline after peaking in ~2000. 

Sunspot time-integral [normalized] shown in green, global temperature anomaly shown in red. Plot here for yourself. 

Clearly, there is no relationship between accumulated solar energy and temperature, so it must be man-made CO2.