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For any period of global warming that is primarily caused by increased carbon dioxide levels in the atmosphere, the laws of both physics and logic require all three of the following conditions to be true:

The temperature of the troposphere must increase at a faster rate than that of the lower atmoshpere
The rise in the levels of atmospheric carbon dioxide must be followed by an increase in global average temperature, and
The rise in global average temperature must be preceded by rising levels of atmospheric carbon dioxide.

Unfortunately for those who have ulterior, political motives for having you believe that global warming is caused by human production of carbon dioxide, none of the three necessary conditions hold:

Since satellite measurements began in the 1960s, at no time did the temperature of the troposphere ever increase at a faster rate than that of the lower atmosphere--in other words, to believe that global warming is caused by increased levels of carbon dioxide is to believe, for no known reason, that the laws of physics do not apply in this special case
There have been many periods, such as the last 9 years since 1998, and also the period from the 1940s to the 1970s, when increasing levels of atmospheric carbon dioxide have not been followed by increasing average global temperatures--so either the laws of logic do not apply, or else increased levels of carbon dioxide do not cause global warming, and
The ice core data show that carbon dioxide levels almost always rise only after a preceding rise in average global temperatures--so either the laws of cause and effect are reversed, or else rising levels of carbon dioxide are not a cause of global warming, but are instead an effect thereof.

From the article Up against the warming zealots:

To the utter dismay of the global warming lobby, the world does not appear to be getting warmer. According to their own figures (from the UN-linked Intergovernmental Panel on Climate Change), the temperature has been static or slightly declining since 1998. The satellite data confirms this. This is clearly awkward. The least one should expect of global warming is that the Earth should be getting warmer.
Then there's the ice-core data, the jewel in the crown of global warming theory. It shows there's a connection between carbon dioxide and temperature: see Al Gore's movie. But what Gore forgets to mention is that the connection is the wrong way around; temperature leads, CO2 follows.
Then there's the precious "hockey stick". This was the famous graph that purported to show global temperature flat-lining for 1000 years, then rising during the 19th and 20th centuries. It magicked away the Medieval warm period and made the recent warming look alarming, instead of just part of the general toing and froing of the Earth's climate.
But then researchers took the computer program that produced the hockey stick graph and fed it random data. Bingo, out popped hockey stick shapes every time. (See the report by Edward Wegman of George Mason University in Virginia and others.)
In a humiliating climb down, the IPCC has had to drop the hockey stick from its reports, though it can still be seen in Gore's movie.
And finally, there are those pesky satellites. If greenhouse gases were the cause of warming, then the rate of warming should have been greater, higher up in the Earth's atmosphere (the bit known as the troposphere). But all the satellite and balloon data says the exact opposite. In other words, the best observational data we have flatly contradicts the whole bally idea of man-made climate change.
They concede that CO2 cannot have caused the warming at the beginning of the 20th century, which was greater and steeper than the recent warming. They can't explain the cooling from 1940 to the mid-'70s. What are they left with? Some mild warming in the '80s and '90s that does not appear to have been caused by greenhouse gases.
The whole damned theory is in tatters. No wonder they're defensive.

I've done some analysis on the revised series. My conclusions, FWIW -

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.