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The problem with this picture is simple: solar activity has declined over the past few decades from a historic peak in 1957 until a century-long low was reached in 2009.
But not quite so simple. We know the earth system, i.e. the ocean, is a heat integrator. I suspect it would be more appropriate to take some running total (sunspot number or area, perhaps) over a multi-decade period and then introduce a lag of, say, 20 years. That is conceptually much more interesting than the current number of sunspots or TSI.
Yes, this is true, and there is some lag in the correlation (after exams wrap up this week I will see what I can come up with regard to more quantitative figures).

I found a source for historical sunspot area data
I used area after recently reading the Livingston and Penn paper on the decreasing size of sunspots. Also, I thought larger area mean a higher proportion of UV, larger coronal holes and a stronger solar wind (but I could be wrong).

At any rate, from the annual average sunspot area I subtracted the mean value of 620 so that the number would be positive during large sunspot cycles and negative during quiet sunspot cycles. A running total was calculated from the beginning of the data in 1875 on the theory that the oceans act as an integrator.

The correlation with the HadCRU4 temps was good, with an r-squared value of 0.74, and including the Sato aerosol index bumped it up to 0.75. Including an ENSO index should get the correlation up higher, better matching the El Nino induced temperature wiggles. Including carbon dioxide levels will most likely also improve the fit, but CO2 is not necessary to get a decent fit to the rise of temps in the late 20th century. The running total of the sunspot data peaked about ten years ago.

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