Given values a and b in the appropriate color space, does perceptual psychology provide an algorithm to determine which is cooler and which is warmer? Even better, is it possible to determine how much warmer the warmer color is?
To resolve confusion, understand that there are two kinds of "color temperature": physical ("scientific") color temperature and artists' color temperature. I am writing software to aid digital painters, so I am concerned with the latter.
Physical or Scientific Color Temperature
This is the mapping between light sources' hues and Kelvin temperature values. It is based on a canonical curve in chromaticity space defined by the color of the light emitted by a black-body radiator as its temperature increases. The mapping from Kelvin to color is trivial via a priori knowledge of this canonical curve.
Mapping from color to Kelvin is harder, requiring the approximate determination of "closest correlating temperatures". Given a light source with known color and unknown color temperature, one finds the nearest point on the canonical black-body radiation curve and chooses the associated Kelvin value.
In brief, physical or "scientific" color temperature is just about assigning Kelvin values to light sources. For more information, see http://en.wikipedia.org/wiki/Color_temperature.
Artists' Color Temperature
Artists' color temperature is arcane, intuitive, and weakly explained in almost all the literature I have encountered (the notable exception being Bruce MacEvoy's online article, which I mention in my answer below). The ambiguous nature of artists' color temperature probably owes to an anti-scientific cultural vein among contemporary illustrators.
The best I can explain is that illustrators generally believe colors like blue and green to be cool and colors like yellow and red to be warm. With practice, artists learn to see temperature differences between colors. Success in representational art depends on being able to see temperature relationships and mimic them with paint. For instance, in portrait painting, an artist needs the facility to make observations like, "Ah, the shadow side of my model's cheek looks warmer than the tip of her nose. I need to make sure that the paint I use to represent her nose has less yellow/red in it than the paint I use to represent the shadow side of her cheek".
I hope it is clear that physical color temperature may or may not be orthogonal to artists' color temperature. They are principles taken from communities with almost a null intersection. Part of the reason I asked this question was to find out if the two definitions of color temperature can, in fact, be treated interchangeably.