GIMP apparently uses a very simple algorithm for automatic white balancing.
http://docs.gimp.org/en/gimp-layer-white-balance.html
The White Balance command automatically adjusts the colors of the active layer by stretching the Red, Green and Blue channels separately. To do this, it discards pixel colors at each end of the Red, Green and Blue histograms which are used by only 0.05% of the pixels in the image and stretches the remaining range as much as possible. The result is that pixel colors which occur very infrequently at the outer edges of the histograms (perhaps bits of dust, etc.) do not negatively influence the minimum and maximum values used for stretching the histograms, in comparison with Stretch Contrast. Like “Stretch Contrast”, however, there may be hue shifts in the resulting image.
There is a bit more tweaking than is described here since my first attempt at implementing this works seems to work for most photos but other photos seem to have artifacts or contain too much of either red green or blue :/