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).
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.
Kevin Cowtan  has posted on biases during the war years here and here. John Kennedy  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.
The residual is more of a ocean effect than land as shown in Figure 5 below.
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):
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.
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.
If what Kennedy says is correct, ship crews didn’t fuss with the trailing buckets as they had other concerns (see Figure 9). The evidence points to temperatures being high during the WWII years because the thermometers were near the engine room intakes.
Following the advice of Kennedy, if I provide a compensating correction of +0.1C to the CSALT model, the model residuals trends more to white noise over the entire record (see Figure 10).
The Power Spectral Density is shown below:
Figure 12 below shows the final CSALT composition with a detrended Arctic component filling in the 1938 and 1944 lobes.
The Arctic component is a new feature of the CSALT model. That and a NAO component help fill in some of the gaps in the overall fit. The correction is not large enough to change the contributions of the other CSALT components except for the aerosol and less so the angular momentum, indicating that the Arctic is sensitive to these factors as a result that these have on melting ice.
The WWII temperature anomaly numbers are suspect as the CSALT model also substantiates. The CSALT model has the largest residual in the early 1940′s. This spike sticks out like a sore thumb on the GISS series as well as the other global series such as HADCRUT.
Using the suggestion by Kennedy and Cowtan to eliminate this bias, we find that the model actually predicts that this is an instrumental measurement error. Eliminating this source of error is one of many reasons that models find applicability as it rejected the WWII anomaly as an aleatory effect.
Also see Uncertainty in SST Measurements and Data sets where Cowtan and Kennedy are reviewed.
 K. Cowtan and R. G. Way, “Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends,” Q.J.R. Meteorol. Soc., p. n/a–n/a, Nov. 2013.
 J. J. Kennedy, “A review of uncertainty in in situ measurements and data sets of sea‐surface temperature,” Reviews of Geophysics, 2013.
 M. Lockwood, “Solar influence on global and regional climates,” Surveys in geophysics, vol. 33, no. 3–4, pp. 503–534, 2012.