I'm looking for a lighting algorithm that produces realistic lights expressed in kelvins, from about 2500k to 6500k. What I'm confused about is how to make the lights properly interact with the colors of game objects.

If a whole level is fully lit (overcast daylight) then it would seem that I should use just the color of the object. But what if I'm in a closed room with no windows, and there is an incandescent bulb shining light in the room? How would that light properly light up the objects in the room?

There does not seem to be an obvious solution to the problem. And simply mixing the color of the light with the colors of the object, seems an inaccurate approach.