Hi
the effect of light spectra on plant growth is a pretty complex issue. I can't answer the question fully but I can help point out some of the important factors. To make things a bit easier lets split the problem into
smaller, more manageable parts.
1. How does the spectrum of light (colour) affect the rate of photosynthesis?
2. How is the colour of light affected by the "emision temperature"?
3. How does the rate of photosynthesis affect plant growth?
1.To start with let's trace the light as it leaves our light source. Light is emitted in discrete packets called photons, you can imagine those photons as tiny little spheres filled with energy if you'd like. This energy is carried from place to place by the photon. The amount of energy the photon carries can be different, these different energies are what we perceive as colour. Blue colored photons carry more energy than red coloured photons.
fig.1 Colour and energy of photons.
You may be tempted to think that therefore it would be best to use just blue light as it carries the most energy, it's not quite as simple as that. Our ultimate goal here is to make sure that as many of the photons emitted by the lamp as possible trigger photosynthesis. This means that we want as many photons as possible to be absorbed by the plant and then to contribute to photosynthesis. This is quantified by the "absorption spectrum" and an example can be seen below.
fig.2. Chlorophyl absorption spectra.
Finally, the photosynthetic system is not a simple one. Absorption of photons can be done by different molecules within the plant and the chance of this leading to photosynthesis is not the same for every case. The chance of photosynthesis taking place after absorption is also related to the colour of the photon. This is quantified by something called the "action spectrum" for photosynthesis(1).
fig.3. Photosynthetic action spectra.
So there you have it. To use your light efficiently it must be of appropriate energy to be absorbed AND of appropriate energy to trigger photosynthesis. From the above spectra it seems that blue and red light are pretty good ad doing both. There are of course other issues to consider, different colours of light may be responsible for different triggers in a plant, e.g. flowering.
2. Colour temperature can be a little bit of a vague characterisation of a light source as it only tells you about the "effective" colour of light that comes out of your lamps. Sure you know that "cool white" will probably have more blue in it than "warm white" but it is not the case that the consituent colours of this white light will be the same for an LED as they are for a fluorescent lamp. To answer your question it is more informative to look at the actual emission spectra of the lamps you are considering. Since most LED's on the market are made in the same way (blue LED with phosphorescent material on top) you can safely assume that what you find online will match up with the emission of your lamp.
fig.4. LED emission spectra for different colour temperatures.
You can see that the "colder" you get the more the red emission is favoured and the less blue light there is.
3. This is the big question. How does all of this add up to your plant growing and being happy? I'm not a biologist and my knowledge in this field is pretty limited but I do know that links have been made between the rate of photosynthesis and rate of plant growth(2). I also know that it is not the whole story. Some wavelengths are needed for triggering different events in a plant's life e.g. flowering.
From my experience I can tell you that CCT of 6500K is good for growing N. ventricosa x ampullaria, some species of sphagnum moss, cephalotus follicularis and heliamphora minor. These can be treated as case studies as I have not done any real experiments on those plants. I'd love to see a discussion here on the forum relating to this question. For those interested in a little bit of reading those are some of the articles I've found on the matter(3)(4)(5)
(1) "BIOLOGICAL ACTION SPECTRA" Holly L. Gorton.Department of Biology St. Mary's College of Maryland.
http://photobiology.info/Gorton.html
(2) Does Enhanced Photosynthesis Enhance Growth? Lessons Learned from CO2 Enrichment Studies. Plant Physiology Jan 2011, 155 (1) 117-124; DOI: 10.1104/pp.110.166819
(3) Journal of Experimental Botany, Volume 58, Issue 12, 1 September 2007, Pages 3099–3111,
https://doi.org/10.1093/jxb/erm130
(4) Journal of Experimental Botany, Volume 48, Issue 7, 1 July 1997, Pages 1407–1413,
https://doi.org/10.1093/jxb/48.7.1407
(5) Journal of Experimental Botany, Volume 58, Issue 12, 1 September 2007, Pages 3071–3077,
https://doi.org/10.1093/jxb/erm251