To a first approximation it is white noise.
There is a modest sign of 3 year periodicity in the power spectrum, cold warm warm, but nothing too significant there.
There are definite long periods revealed by moving averages. From the series start in 1880 to WW I, the series is stationary. From WW I to the end of Korea, it is increasing. From the end of Korea to the end of Vietnam, is it decreasing. From the end of Vietnam to now, it is increasing. I am being deliberately vague about the timings because only long periods are correct for moving averages.
The up and down movements in the long periods are of the same magnitude and duration. The overall series goes from low to high because it contains 2 ups and 1 down. A regression line or other fit (I used cubic and sin based fits as well as lines, all give broadly similar slopes) shows a net rate of increase of about 1 degree C in 200 years. If you measure peak to peak or trough to trough, there is no trend.
Plotting the histogram of departures from the mean, normalized to standard deviations, gives a roughly symmetrical distribution with most of the observations well concentrated between +2 and -2 sigma, with no trend. Adjusting for a linear trend instead, or for a sin fit or polynomial fit trend, in each case results in a skewed distribution with far more observations between 0 and -1 standard deviations (of the detrended series) than of positive ones. It also gives more +3 sigma events and a longer tail on the up side (because it classifies early warm period 1930s events as larger departures from the still-low trend).
If this is a noise signal it is therefore more likely stationary than trending. If it supposedly does have a trend, that trend (over cycles) is modest, with an expectation for the next century of an additional increase of 0.5C. And in that case, it is not pure noise about a mean temperature, but skewed with cooler cases more common, balanced by high outliers.
I note that the scale of increase seen in the second part of the series, when higher CO2 is observed, is roughly the same magnitude as can be accounted for by the Stefan-Boltzmann law with no amplifying term or "climate sensitivity". If one looks only at the last uptrend and ignores the rest of the data, one might detect a climate sensitivity around 2-3, but certainly nothing larger. This implies future temperature increases from additional CO2 greenhouse are bounded at about 1-1.5C. And it requires "believing" the current uptrend while ignoring the previous downtrend period, or the previous uptrend period that cannot have been caused by CO2, since CO2 hadn't risen yet.
The natural variations before CO2 can have been operating are equal in magnitude to anything it can physically cause, and random in sign. There is no reason to expect that they have ceased, or that later movement is all attributable to CO2 when none of the early moves (in both directions) were. Therefore, there is no reason to expect anything beyond the direct power terms CO2 can provide directly, which means under 1C changes ahead, maximum.
It is useful to actually quantify the total extra power reradiated by the warmer earth, if this series were taken as representative of the whole earth and the data is reliable (UHI effects ignored for the sake of argument etc), during the previous "up". And likewise to quantify the total energy shortfall from the higher peak to peak level, involved in the lower series from early 50s to mid 70s.
The peak to trough power level varies by about 1% (SB law, 0.7 degrees, 291C base), looking at a long moving average not the year to year noise. We can appoximate the integral of the power as a triangle, with a base 60 years long (roughly 1916 to 1976, for the up and the down combined) and the peak that high.
Let the operating power be somewhere between 250 and 500 watts, then the 1% difference is 2.5 to 5 watts at the max, half that as an average, and operating for that length of time. Then the total excess energy for the "pulse" is 1.2 to 2.5 times 10 to the 23rd, Joules. That is about 20000 exa-joules, or 44 times current world energy consumption. Which was of course significantly lower in the past, but then the period of the pulse is 60 years. Same scale in other words.
Similarly we can measure the shortfall of the cooling period (the "V" made from the Korea peak to the present peak with a 70s trough in between). The baseline in years is about 10% shorter, that is all, so the total energy is about 10% below the previous figure but the same order of magnitude.
This suggests another simple "null" hypothesis, beyond the null SB effect of known increases in CO2 - as humans release energy for their own purposes, the earth has to warm very slightly to glow slightly hotter for a period on the order of a few decades, to reradiate the released energy into space. Keep releasing stored energy at the same rate and you will maintain the marginally higher temperature - there is a human power input term. If so, we should expect to see a modest uptick in the mean temperature as the power "switches on". This is an adequate explanation of the observed regresssion line.
Still does not explain the full fluctuation in the moving average about that average, however. Solar or natural weather driven variations are the likely causes, but certainly not something that starts around 1950 and pushes one way the whole time, as CO2 does.
My inconvenient truth is that vast strides towards alternative energy and improved technology have occurred during the Bush regime, not under Democrats.