You would need to do a color space white point conversion in L*a*b* space. Most color models that we normally work with, primarily RGB but often CMYK, are designed to support the limitations and requirements of physical hardware. Those models usually don't represent the "perceptual" space of color very well, though, and white point is definitely a perceptual aspect of color.

Whenever you need to apply perceptual adjustments to an image, such as color temperature or tint shifts, it is best done by converting from RGB to XYZ, and during the conversion, you can apply "reference white points" for the source and destination color space. Conversion from XYZ to Lab then gets you into a color space where you can perceptually remap the white point and all the colors such that they maintain continuity.

Color space conversions, chromatic adaptation, white point adjustments, etc. are rather complex mathematically. The more perceptually accurate you intend to be, the more complex the math usually ends up. An excellent source of information for color space conversions can be found at Bruce Lindbloom's web site. Some additional useful information can be found on Wikipedia. You might also find this information on CIE's D-Series Illuminants useful, as it contains white point specific information, calculations, and constants.