Warm and cold tones together, and complementary colours together, will generally have the same effect: contrast. It depends on how much you want, how subtle or strong the individual colours will be, what the dominant tone or colour will be. E.g. the pale blue (reinforced but not overwhelmed by the darker robe lining) and yellow of the left-hand wizard, contrasting with eachother and with the stronger red accent colours. It's a three-colour split with the three primaries rather than a two-colour split, which also affects the degree of contrast, but you get the idea.
Then there's the other wizard who's nearly all warm yellows and oranges, so that the saturated green gem on his dagger pommel jumps out a lot more than the bigger, similarly-saturated red gems in his staff and dagger quillions.
Complementary colours can be mixed, and generally 'cancel' eachother, creating a darker, more greyed-out, or muddier tone. They can be used to create subtle shading effects beyond 'a darker tone of the main colour', though I think it's more commonly used with washes and glazes than directly mixing colours into layer shades. It allows light to pass through the transparent or translucent layers, pick up the colours as it bounces back out, and lets your eye do the mixing, with less of the muddying effect of direct mixing.
I haven't thought much about the effect of warm shadows and cold highlights on minis, but it reminds me of the lighting in certain brightly sunlit scenes. Downward-facing planes pick up warm reflected light from the ground (particularly yellow-to-reddish soil or rocks), upward facing planes (though still on a shadowed side) pick up cool tones from the blue sky. 'Proper' highlights are, of course direct, bright, warm sunlight. Could be used in a kind of
OSL effect on minis.
To be honest I can't go too in-depth with my basic understanding of these concepts;
but I know a man who can.
