For instance, I live in a row house. The south facing windows have shades over them, which I can't remove because I'm renting. This means the amount of natural light is extremely limited inside. I find that if I don't spend some time in the sun early in the morning, I feel extremely sluggish and lethargic.
Replacing the sun is really hard though. Not only does the sun have a "perfect" CRI, but it is extremely bright and provides a very diffuse light. (Not to mention, the sun is really cheap). I've found the easiest way to mimic the diffuse nature of sunlight is to have a number of light sources.
Right now, the only "sunlight" (7500k+) bulbs that I can find that are inexpensive enough to cover my living room, render color well, and are efficient enough to keep on during the day are florescent. Halogen uses too much power and generates too much head. I can't seem to find reasonably priced LEDs with a good CRI above 5000k.
I've only been able to find 2 kinds of "sunlight" LEDs. One is 75-watt BR40 (or lower wattage BRxx lights), which, as spotlights, are not very versatile. The other are "grow-lights", which I am hesitant to buy, since I have little interest in partaking in a no-knock raid at 2 AM. That might be paranoia, but I've heard stories at the homebrew/hydroponic store where I buy my homebrew supplies, and I don't think it's too unlikely.
http://www.topbulb.com/color-rendering-index
that graphically shows the color distribution. Temp is where on the visible color spectrum its focus is.
For example, if you're looking to replace your household tungsten lightbulbs then it's really important to pay attention to the R9 value that your LED ilght has (1), as it refers to the red value being emitted by the bulb and is what affects skin-tones.
And, yes, CRI is completely independent of temperature. You can have a daylight or tungsten LED bulb with completely varying CRI values.
(1)http://www.eyelighting.com/resources/lighting-technology-edu...
These 5100K, 90+ CRI bulbs in your kitchen -- are they fluorescents or LEDs?