So lets say if you compare the color temperatures of 2500 K vs 5000 K, the 2500 K would have more red light and usually is described as “warm” light, even though it is called a lower temperature at the same time.
(Yeah I know the color temperatures in Kelvin have smth to do with black body radiation, but I wonder if the red light = warm and blue light = cold has some evolutionary background or that blue light has been discovered wayyyy later (blue LEDs etc.).)
TL;DW: Most lights used to be hot glowy things, e.g. fire, light bulbs or the sun. Those start glowing red hot at relatively low temperatures and become white hot at high temperatures. That’s where the inverse scale comes from.