According to the CSALT model, which fits the temperature series data over the last 100+ years, the most significant anomaly encountered is a warming peak that occurred over the WWII years.  This spike is only weakly associated with a SOI peak and is suspicious as it corresponds to missing temperature readings during the war years (see Figure 1 below from IPCC).

Fig 1 : The geospatial distribution of surface temperatures. The interval from 1940 to 1945 shows the Northern Hemisphere dual warming spikes along with an ENSO El Nino event in the Southern Hemisphere. These regions do show warming but they may also have a common warming bias.

The significant SOI event occurs in 1941 which  show up in the data, but the warming lobes in 1938 and 1944 are correlated with Northern Hemisphere, Arctic and NAO events. In Figure 2 below, the residual of the CSALT fit has peaks which corresponds to GISS Arctic temperature anomaly peaks.

Fig 2 : The CSALT residual shows a clear alignment with the Arctic temperature anomaly.

Kevin Cowtan [1] has posted on biases during the war years here and here. John Kennedy [2]  writes that the uncertainties are “particularly large in the period surrounding the Second World War owing to a lack of reliable metadata”.  Kennedy further writes that “During the war years 0.2K was added to reflect the additional uncertainty during that period”

This is an uncertainty level and not an offset, but it is curious that the only time that the CSALT model residual error stays above 0.1K for any length of time, and actually reaches 0.2K is from the years 1938 to 1945.  See the middle panel in Figure 3 below.

Fig 3 : Points P and R are the largest residual anomaly in the CSALT fits. The region in between P and R is a known SOI event which the model is regressing against to minimize the residual error.

Fig 4 : The largest residual is located during the WWII years, 1938-1945.

The residual is more of a ocean effect than land as shown in Figure 5 below.

Fig 5 : The anomaly is more apparent on sea data HADSST3 (upper panel) than land data CRUTEM4 (lower panel)

It appears that the peakedness of the WWII anomaly is due to contributions from the Arctic zonal region in the lobes and the SOI in the center. The CSALT model residual of the GISTEMP series has dual spikes that straddle a broad Arctic peak during the war years (see Figure 6):

Fig 6 : The Arctic temperature records, north of 60 degrees latitude, show a clear hump that may be related to measurement biases during WWII. This is also clearly seen in the CSALT residual shown below.

On the right hand side of Figure 7 below is a finer resolution which highlights the two spikes occurring at 1939 and 1943 in the Arctic and how they line up with the CSALT model residual spikes.

Fig 7 : On the right is a finer resolution of the Arctic GISS readings. The two residual spikes correspond to Arctic spikes.

The CSALT model does not use data that is specific to the Arctic so that the temperature anomaly could possibly be of a mechanism other than one of the CSALT indices such as the NAO (North American Oscillation) index, or it could be a measurement error in the Arctic. Also it is known that the mechanism of Arctic amplification will amplify the noise.

One bias that John Kennedy and Kevin Cowtan have isolated accurately is a potential measurement error between 1940 and 1945 (see Figure 8 below).  It is not clear whether the time series such as GISTEMP actually correct for this.