According to Wikipedia.. Color temperature is a characteristic of visible light that has important applications in photography, videography, publishing and other fields. The color temperature of a light source is determined by comparing its chromaticity with a theoretical, heated black-body radiator. The temperature (usually measured in kelvin (K)) at which the heated black-body radiator matches the color of the light source is that source’s color temperature;
“The Kelvin Scale (K) can be used to define a relationship between the heat property of the light and the color. The lower the Kelvin temperature, the warmer (red/long wavelength) the light, while the higher the number, the cooler (blue/short wavelength) the light.” - Camera 101 -White Balancing

Here is a list of Light Sources and their Color Temperature.
1700 K Match flame
1850 K Candle flame
2800–3300 K Incandescent light bulb (75w, 100w, 200w)
3200 K 500 watt tungsten lamp
3350 K Studio “CP” light
3400 K Studio lamps, photofloods, 500 watt photolamp
4100 K Moonlight, xenon arc lamp
5000- 5400 K Horizon daylight
5500 K Photographic Daylight
5500–6000 K Typical daylight, electronic flash
6500 K Daylight, overcast
9300 K CRT screen
Why is this scale useful? It will help you keep your whites whiter and that is important in any shoot.. if you see the color cast on the photo, you can easily compensate by adjusting the Kelvin scale to increase or decrease the color temperature depending on your requirement.
Is AUTO White Balance fool proof? I am afraid not.. in certain mixed lighting conditions, the mix of light may be too bluish or orangish.. depending on which is the more dominant light source. You will have to adjust the kelvin scale on your camera to get a good balance between light sources. a shorcut would be to do a custom white balance against a white surface or a gray card or even use a EXPODISC (sample shots here).
Are their other uses of Color Temperature? Yes.. you can do creative photography by using color balance to change the mood of the photo to make it warmer.. or cooler depending on what you want to convey to your viewers. You can actually cool down a sunset by changing the white balance.. try it..from warm sunny skies you will get a cold blue sky..
Here are 3 photos using Different White Balance Settings.

using the EXPODSIC

Using Auto white balance

Using Incandescent White Balance.
For record purposes i submitted the first photo to get the proper colors.. but the last one has more mood into it and made it look more warm and cozy… which one do you prefer?
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The reason I write about this is to give basic sample of how sensor sizes affect the final image. as you can see in the first image, sensor sizes arent created equal and so far the 35mm film sensor size is limited to a few brands.

