Are you looking to change the color of the sun in your photographs, or simply represent the color that is there accurately? The two are very different tasks. The former would probably require a lot of work, and I'm not sure it would actually be accurate. The latter is actually already taken care of for you with ICM and ICC profiles.
It should also be noted that "white" is a highly subjective thing. The "white" of your monitor would, technically, be too blue for a "true white", given that 6500k models daylight, not sunlight. The white of the sun as imaged directly, without the interference of an atmosphere or any filtration, is probably more accurately modeled at 5785 K in the photosphere on a normalized basis, but it can fluctuate between around 4000 K and 6000 K depending on location and time (sunspots tend to be cooler). There is also the Chromosphere, above the photosphere, which ranges from about 6000 K to tens of thousands of degrees Kelvin until you hit the Corona, which spikes into the millions of degrees. When you image the sun without a filter, the only time your actually photographing the photosphere would be through sunspots, otherwise the white point of the sun can fluctuate wildly over its surface. With a filter, your ultimate white point will be affected by its design and the wavelengths it actually is designed to pass through, so again nailing down an exact white point is probably going to be a tough thing to start with. A neutral, true white to the human eye is probably in the realm of 5500 K, however that actually changes depending on whether you are observing an emitter or a reflector.
Image Color Management, or ICM, is a system that is designed to manage the proper, accurate conversion of color information from one color space (say, RAW files from your camera) through the color space of your editing software (say, Photoshop, with is standard D50), to the color space of an output device (say, a computer monitor). You should not actually have to do anything specific at a low level to achieve the correct color balance, assuming your screen is indeed calibrated correctly. So long as you trust the accuracy of your imaging device, and trust the accuracy of your screen, if you use fully color-managed software like Photoshop, you should not actually have to worry about manually tweaking the color of your photos at a pixel-level. Adobe Camera Raw and Lightroom both include a color temperature adjustment tool (as well as a tint tool, however tint in photographic editing is for the opposite axis, magenta-green, and should only be used to correct the usually slight divergences along that axis most often caused by light produced from an electric gas discharge...i.e. fluorescent light.) If you set the color temperature slider to 5785 K, or within that realm, the color of the sun's photosphere as represented on your screen should indeed be very accurate for your state of calibration.
Last, but not least, you should be aware that the color balance of your photos will only be accurate as you intend them to be on your own system. The average user does not calibrate their screens, and as such, representation can vary widely. Many calibrated screens are to a 6500 K white point, however many photographers calibrate to 5000 K to match Photoshop and make natural fiber prints be more accurately represented on screen. Personally, I would consider a screen calibration to 5500 K to be more "white point balanced" than 6500 K (which is definitely bluer). If you want as much accuracy as possible, I would say calibrating your screen to 5785 K, and adjusting your photo white balance to match, would produce the most natural white possible, at least relative to the sun.
As an aside, if you really do want to manage white point conversion yourself directly on every pixel in your images, then you should look into the work done by CIE. They have been doing work on illumination, illuminants, color theory, color conversion, color modeling, and color space definition since the early-mid 20th century (1913 on). The L*a*b* color space (Lab) for short, is the quintessential model of human perception of light and color. It is the crux of color space conversion and transformation. XYZ is a critical modeling space that is used as an intermediary step when converting from RGB into Lab, then back out of Lab into some other color space (which may also be RGB but simply with a different white point.) You can find quite a bit of information on Wikipedia about CIE, Lab, XYZ, etc.: