Lowel Lighting have written a great article that takes the confusion out of colour temperature and color rendering index.
Color Temperature Defined
Color temperature has been described most simply as a method of describing the color characteristics of light, usually either warm (yellowish) or cool (bluish), and measuring it in degrees of Kelvin (°K).
That’s a little too simple to be of more than introductory value.
A more technical definition assigns a numerical value to the color emitted by a light source, measured in degrees of Kelvin. The Kelvin Color Temperature scale imagines a black body object— (such as a lamp filament) being heated. At some point the object will get hot enough to begin to glow. As it gets hotter its glowing color will shift, moving from deep reds, such as a low burning fire would give, to oranges & yellows, all the way up to white hot. Light sources that glow this way are called “incandescent radiators”, and the advantage to them is that they have a continuous spectrum. This means that they radiate light energy at all wavelengths of their spectrum, therefore rendering all the colors of a scene being lit by them, equally. Only light from sources functioning this way can meet the truest definition of color temperature.
The above is not a true Color Temperature chart. Instead it is a hybrid, showing the color temperatures of light sources most commonly encountered in professional imaging. In our scale, tungsten-halogen has a color temperature of 3200°K. Household fluorescents are accepted to be around 4500°K, depending on the lamp.