I found out that the colors of the LCD display on the Nikon D600 are influenced by the "auto" monitor brightness setting and by ambient light. If monitor brightness is set to auto, then in bright light outdoors, the colors can look very warm with a yellow-orange tint. I don't know if this is just my D600 or all D600 units. If you want to check for this effect here is how I did it.
To do this test, you need to be in a place where you can be in bright outdoors then move to somewhat dim indoors.
1. Set the monitor off delay (option c4) to 1 minute or longer. Set the monitor brightness to auto (in the setup menu).
2. Take a shot, preferably a headshot.
3. Go into bright ambient light outdoors and view the shot.
4. While still viewing the shot, move to a dimly lit indoor location. The colors will not change.
5. While still viewing the shot, press the play button to turn off the viewing then press it again to see the shot again. The auto brightness will compensate for the lower ambient light but in addition you may see that the colors are more neutral.
Don't forget to restore your monitor off delay and monitor brightness to its previous setting.
The practical consequence of this is that if you're using auto monitor brightness, be aware that the colors may look warmer when you're in bright ambient conditions but that your actual white balance might be correct.