Why do we use temperature to describe the color?

When we buy LED lamps, their packages always say what color temperature they are, like 2700K, 3000K, 5000K etc. We may wonder why use temperature to describe the color.

When a black body, like iron, is heated up, its color will change according to the temperature that it’s heated to. It turns out that this range of color is very useful for describing the color of light.

The color of the iron will become black under 700 Kelvin. Keep heating up, it turns red if gets heat enough. The iron starts to glow orange if you heat up more.

When the iron’s temperature reaches 2700 kelvin, its color will approximately match the color of light emitting by the incandescent bulbs. Heating more even it will melt, what temperature it has, what color of light it call.