There is indeed disassociation between colour temp and spectrum. You'd be thinking of colour rendering (CRI)
http://en.wikipedia.org/wiki/Color_rendering_index
It's not a perfect rating(by any means) but for now, it'll do until everyone agrees on a new standard.
Cree started naming the colour temperatures.. Warm White 2600 - 3700K, Outdoor White 3500 - 5300K, Neutral White 3700 - 5000K, Cool White 5000 - 8300K
Incandescent bulbs are generally warm white, fluorescent tubes are usually cool white. Warm white is generally more yellow/orange, and cool white is more blue.
Everyone has different preferences though, it's best you first dig up a specific colour temperature, then try to get the best CRI you can, either by mixing multiple LEDs (White LEDs are notoriously low in reds/ambers), or purchasing high CRI emitters. Nichia is good for high CRI emitters. Cree is good for best efficacy (they're working on colour, too, look up the Cree LED bulb. They're dirt cheap and an excellent value for the price- USA only, IIRC). Luxeon? They seem to be focusing on emitters for the automotive market.
As for replacing the array in your light - what kind of driver is in there?