Color Temperature Blending
One fairly obvious method of handling a scene lit by different types of light source with opposing color balances is to treat it as two (or more) layers, one for each light source.
The principle is to concentrate first on color correction for each light-source layer at a time, and save the problem of combining them until later. Thus, for one image layer, you should focus entirely on only one light source, ignoring the effects this has on parts lit by any other source. For the next layer, do the same for the other light source. With three or more different light sources this can become unnecessarily complicated, but with two it is perfectly manageable.
The color adjustment method can be any of the ones discussed previously, ...
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