Colour temperature
in the camera when you manual change color temperature for white balance you are changing to compensate for the color temperature of scene you film or photograph so if there is a object that is white in color in the scene the camera sees it as white color and not other color. so if the light shine on the white object is blue light (cold) you need to tell teh camera that the camera the artificial light on the object has blue color and compensate so that the camera sees the white object as white or if light is red (warm) is the same concept. this is why you think the info of color temperature you find on google and what you see in camera is opposite.
if you photograph in a room with painted white walls and has incandescent light bulb lamps which to our eye look yellow and in the camera you set white balance kelvin to low number like 3000 when you look at the photo you take the colors of the room walls appear white because you are telling the camera that it is taking photo of place where the ambiant light is warm. but if you change kelvin to 10000 for the same room with the same lights the photo looks super orange it happens because you make the camera think the lighting of the room is cold so the camera compensates (with error) to compensate for the light to get correct color of the wall.

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