If there is more than one light source, they should be the same temperature, right?
If this isn't always the case, when should they be different?
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Generally speaking yes. This makes it easier for your camera to define the correct colors. Normally you gain experience best by committing errors or by analyzing the errors of others. So, if you see an image that is too cold, the color temperature / white balance should be higher. If it's too warm, the color temperature should be lower.
If you have two different light sources, you must prioritize: Which part of your scene should have a neutral color temperature / white balance, which could be different.
And here are the creative exceptions: If you analyze movies or professional documentaries, you realize that there aren't many neutral, correctly white balanced shots. Because they look boring. So, if you only have different light types, why not use them to compose your scene. Just to give one example: If you compose a scene and want to present an actor or an interview partner in a comfortable mood, he can have some warm light in his face, and a colder light in the background.
It depends entirely on what you are looking for. If you want an image that appears consistently lit, then you will want to have uniform light temperature. If however, you want to have some type of effect lighting, you will want to alter the lighting temperature.
Say for example you have a candle in the scene (or want to allude to a fire off-screen), or perhaps it's a sunny day outside the window. You can use lights of a different temperature and vary their intensity to achieve the desired look of shading with color after white balancing to your key light (the main wash you are using to light the scene).