Looking at the referenced paper again I see where this may have been picked up in my peripheral, from Smith Reynolds 2005:
As with the SST, the simple averages are generally consistent with the reconstruction average. The twentieth-century warming is about 0.6°C.Because of the uncertainty estimates, the warming can only be confidently established between 0.3° and 0.9°C. Compared to the global average of Folland et al. (2001, 2001b), our average is similar over most of the analysis
period.
The more recent paper isn't redirecting from the NOAA website like it was previously. I don't know why?
If you are going by the Smith-Renolds 2005 paper, then you acknowledge the fallacy of your "20th century average" includes 19th century data, as they are quite clear in their distinguishment of 19th century data vs 20th century data.
"...For the nineteenth century, when sampling is most sparse and the error estimates are largest, the differences between the averaged reconstruction and the simple averages are largest...
...The uncertainty estimates indicate that the nineteenth-century anomalies should be used with caution. Part of the nineteenth-century uncertainty is due to bias uncertainty, which could be reduced using future bias corrections that incorporate a better understanding of the historical bias. However, much of the nineteenthcentury uncertainty is due to the effect of sparse sampling on the low-frequency error estimate. In any case, the twentieth-century warming is significant...
...Variations in the LST simple averages in the nineteenth and early twentieth century indicate that these large uncertainty estimates are justified...
...However, there is more uncertainty in the LST average, especially before 1940 when much of the land areas are undersampled. Since we analyzed LST and SST anomalies separately, the similarity between the two is derived from the data, and is not an artifact of the analysis method. Variations in the LST simple averages in the nineteenth and early twentieth century indicate that these large uncertainty estimates are justified. The Jones–CRU LST anomalies
are cooler than the reconstruction early in the record, when sampling is sparse and our reconstruction is more damped. After 1930, those simple averages are more consistent with the reconstruction..."
Many more instances littered throughout that paper,...additionally, while the smith-reynolds analysis is good for what it covers, it leaves out two of the areas that have experienced the most dramatic temperature increases of the 20th century, the latitudes above 60 degrees. The most recent assessment I'm aware of seem to indicate a temp rise of around 0.74
oC (MoE of +/- 0.2) for 20th century (1901-2000) and I believe this comes from the 2008 update of Smith's work (IINM - this still doesn't include high lattitude integration, which would reasonably bump this figure up a few notches).