Okay, you have a laboratory the size of a planet and very limited data to work with in spite of everyone and their siblings jumping on the bandwagon. So you might develop a tendency to cherry pick things that are closer to your wheel house and ignore stuff that doesn't quite make sense. What you need are a few gut checks.
Since we live on a water world warming means more water vapor in the atmosphere. You are not really sure how much, but there pretty much has to be more some where because warmer air holds more water until you reach saturation.
Sea surface temperature averaged over the entire ocean area, which is the energy proxy for the majority of the surface area, doesn't provide any information on how much water should be in the atmosphere. Land surface temperature average (Tmax+Tmin)/2 isn't all that great either for a gut check. If you stick to areas that should have moist air, you can use the difference between Tmax and Tmin, or diurnal temperature range (DTR) and as there is more moisture in the air the range should decrease. Fantastic! BUT! You can also have the moist surface area expand so there isn't much change in DTR just an increase is in the "moist air envelope". Got that? As there is warming of the Earth's surface, area above about 0 C degrees would expand and there would be more moisture in the air, but you have to consider both "features" of the thermodynamics.
When the Berkeley Earth Surface Temperature (BEST) project started, they added some of this information for the average guy on the street to see. Additional Area Above Freezing is a nice thing to see. It reinforces the obvious, that the Earth is warming, but it doesn't explain why. It could be due to Greenhouse gas warming/ black carbon, just plain warming from the Little Ice Age (LIA), improvements in agriculture and snow removal technology or a combination of everything. The increased land area above freezing is about 4 million kilometers square which is around 1% of the global surface area. It would be nice to know the ocean area change, but we don't have that information.
BEST also had a graphic showing how DTR decreased until around 1985, when the new digital Maximum and Minimum Temperature System (MMTS) was installed but I cannot find that on their site very easily anymore. That shift to increasing DTR isn't kosher with the physics you should expect. It turns out there are a few issues with the change from old liquid in glass thermometers and the new digital thermometers. For whatever reason, that issue isn't brought to people's attention very often. What is means though is that there is some bias in the MMTS data mainly related to the Tmin readings which is part of the gut check. Unexpected stuff is supposed to be the fun part of science and when the unexpected stuff is exactly opposite of what you expect it is really fun. Unfortunately, this unexpected stuff could be instrumentation related error which isn't as much fun.
The not so fun part of instrumentation error is the acknowledgement. "I don't know how much we should believe this data." That means figuring out some ad hoc uncertainty margin for the FIIK issue. Engineers are used to a fair amount of FIIK so they have rules of thumb which are "proven" gut checks and safety margins. Scientists, especially very vocal scientists that have already sold the public on their remarkable abilities, tend to have more issues with the occasional FIIK.
Luckily, the Climate Research Unit provides their DTR to KNMI Climate Explorer so we can see the issue. If you are a fan of CO2 done it, the curve down from about 1950 to about 1985 is exactly what you expect to see, CO2 warming is causing water vapor feedback which will amplify the CO2 warming. However, 1985 to present kinda puts a hitch in your water vapor feedback giddy up. The difference is only about 0.3 C or about 0.15 C in Tave so it is only about 0.05 C "globally" but there could be more issues couldn't there? 1900 to 1950 also is a bit different than what we should expect.
The net impact of this isn't much, but then neither is the total warming that can be easily attributed to CO2 equivalent forcing. The more interesting part is the pre 1950 period which has the least accurate data. Many of the earliest land surface temperatures where Tmax only and often only for summer months above the Arctic Circle which wouldn't show any DTR change.
This post is inspired by Greg Goodman's post on Climate Etc. Greg basically noticed the difference in thermodynamic meaning of land and ocean temperatures. As a rule of thumb, the oceans have about twice the sensible heat capacity of the "average" land area. Adding energy to the oceans results in about half the temperature increase that the same amount of energy added to land would produce.
Greg could have gone further and noted that increasing the cold, dry polar areal coverage would increase the difference in specific heat capacity even more changing the ratio. If the areal coverage remained the same, there would be a more consistent reference which could allow the teasing out of more information. But with adjusting the temperatures and changing the area you have a moving reference that isn't very reliable.
You can see that the variance in the chart above gets smaller as you go back in time which can lead to a false sense of precision. Then when the data keepers publish they tend to emphasis the remarkable accuracy they have based on using large numbers of measuring points that didn't exist early in the record. That small 0.05 C could double the amount of uncertainty that they claim based their statistical treatments. A small hitch but large compared to stated uncertainty.
The reality is that the difference in the heat capacity of the oceans and land mass is a feature that could be used to refine uncertainty ranges and allow a bit more accurate attribution, provided there is a standard reference.
I started a few years ago looking into a more standard reference but let it go because of the politics involved. Oceans with the higher heat capacity and the tropical oceans with the majority of the heat content should make a more reliable reference also known as a teleconnection. Using that as a standard, you could compare regional data adjusted for expected amplification based on specific heat capacity. That was the main part of my 2000 years of Climate post.
Since then there have been a number of minor adjustments to the different data sets so I might do it over to see what impact they have had. I had hoped that BEST would have an absolute temperature product by now, but I guess that is still a ways off.
Just remember that this quibbling over a "small" issue is a bit like quibbling over a gun sight being off a quarter of an inch at ten yards. If the gun happens to be a sniper rifle it could miss by a hundred feet at 1000 meters. You need extreme accuracy in references if you are going to project to the distant past.