What is K?
K is a measure of degrees Celsius and is termed the Kelvin scale or absolute temperature scale.
0 degrees Kelvin is approximately -273.16C.
This value (0K) is typically considered the lowest possible temperature in nature.
It is postulated that at this temperature all particle (for example electron) motion will cease.
Note of Interest
Helium which we commonly know as an inert gas also exists as two forms of liquid at temperatures near absolute 0 (0 degrees Kelvin)
Helium I exists at temperatures between 2K and 4K.
Helium II exists at temperatures below 2K.
If Helium I is placed in a Dewar flask (a very, very efficient thermos bottle) and a small quantity of Helium II is placed in the middle of the Helium I the Helium I can be stirred one direction and the Helium II another direction and the liquids will continue “swirling†without interacting.
Why is the Kelvin scale employed in the classification of light?
The short answer is simple – Black Body Radiation.
What is Black Body Radiation?
If a black sphere is heated to very high temperatures the sphere will emit electromagnetic radiation.
At 1000K red light will be observed.
At 5000K sunlight will be observed.
At 7000K blue tinted light will be observed.
At 10000K bright white light will be observed (9300K is the black body temperature of. the light emitted from an analog TV).
Does this seem odd with respect to the typical knowledge of light varying from infrared to ultraviolet – Definitely Yes (and this is where I have been struggling for several months and I hope that I now have a handle on it)
Please reference the following:
http://www.sizes.com/units/color_temperature.htm
Is the Black Body radiation single frequency?
No. The radiation (various frequencies of which humans can observe as light) is emitted in a spectrum.
The following chart is the best exhibition which I could find depicting visible light with respect to temperature.

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Why are aquarium lights rated by temperature instead of much more simplistic frequency or wavelength. (The long answer)
Once again it took me a little while to get what I hope is a handle on this.
Light emitted by our aquarium bulbs is not evenly (normal distribution) distributed about a single frequency.
Hence the concepts of black body radiation and temperatures associated therewith are employed.
TR