Benm
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And the difference between 30,000k and infinity Kelvin would be nearly zero.
That is because people misquote color temperature.
It should the 'spectrum emitted by a blackbody at that temperature', which is fairly accurate from tungsten lamps and 2700K or halogens running closer to 3000K.
This assumption that usable visible light would be emitted when the temperature approaches infinity is nonsense. If you ram up the blackbody temperature to a million or billion kelvin it will still radiate, but with most of the 'light' coming out in the UV and beyond - excellent to set your room on fire, not so good for reading a book by.
As for actual sunlight: in space that is in the order of 6000K, but since some of the blue is scattered in the atmosphere on the ground it's more like 4000K during daytime, rolling down to 2000K or less at sunset depeding on distance to the horizon.