Now just to be clear, this is as much an physics question as much if not more than it's an history question and one that is in a still hot area of weather sciences.

That is not necessarily the world war II. Now let me explain, if you take the graphics from Callendar (1961), Fig.2 you will notice that until about 1920, the temperature variation curve of Chile, Japan and Turkestan show very interesting behaviours when compared amongst themselves. Turkestan's curve demonstrats a striking increase in the temperature variation right around the1925 to 1940, Chile's to a lesser degree starts growing in the end of 1940 and, what's most interesting, Japan' curve remains incredibly constant and starts to grow only near around1945-1950, after which it starts to go down again. Japan showed less variation in temperature than either Chile or Turkestan for a significant part of the conflict.

Also if you look at Smith (2005) work, once again there is no great temperature anomaly in the period compreending the world war II. If you look at the Figure 21 in the work of Hansen (2010), it may become clearer. It's a figure of the mean temperature and in it it's also present the increase of mean temperature in the WWII years that the image you presented shows but it is much clearer that it is just part of a more complex trend.

What I mean is: that anomaly you saw wasn't necessarilly caused by the WWII and there was no sudden variation in the mean global temperature. As I pointed previously, if you take curves of countries that had nothing to do with it they still present high positive temperature anomalies and some countries directly involved don't. I confess I don't know enough to give you a clear answer as to what caused it and why specifically during that time period. There are several factors that influence the global temperature: CO2, climate events, solar activities, etc...

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Notes

I must say you freaked me out with that image. I have been working with Earth's electricity, which is affected by the conductivity of the air, which in turn is affected by the ions in the atmosphere and I just thought "what sort of absurd event happened to change the temperature that quickly? It probably affected the Earth's electricity too".

Here is a curiosity: we can't use electric field data from between the 50's and 60's because the nuclear bomb tests changed the conductivity of the ionosphere.

References

Hansen J. GLOBAL SURFACE TEMPERATURE CHANGE. 2010.

Callendar G. S. Temperature fluctuations and trends over the earth. 1961.

Smith T. M. & Reynolds R. W. A Global Merged Land–Air–Sea Surface Temperature Reconstruction Based on Historical Observations (1880–1997). 2005.