warm/neutral/cool tone of one image
I would like to point that determining the color temperature of the image is still an open problem.
If you convert the RGB image to CIE XYZ Tristimulus color then calculate normalized chromacity to get the temperature, it works for pixel, kinda, it is a lot of effort to simply feed it a mean. Indeed it cannot work. The average over all pixels gives artificial color (if you do it over RGB it is not even chromacity preserving).
Whenever it is possible use CIE RGB (it is physical based color space, using the actual human sensitivity to colors) or some color space naturaly separating hue and lightness like HSL.

perform image segmentation or alternatively perform edge detection and subtract edges from reduced image
take from results only big enough blobs - this is arbitrary and depends on the image resolution, but more than 50 pixels is good default value. Blobs are segments of the image with small inner variance - they pixels are similar to each other, not varying too much in intensity and chromacity.
Calculate the average of blobs in the HSL space. Take into account the area and assign greater weights to bigger blobs (if blob spans over 200px it will be better perceived than 4x50px).
take into account the placement of the blob (calculate how far it is from the center) 
the the center is weight 1, slightly decreases to suddenly drop. This weights reflect what is better exposed (assuming that there are no important features at the corners, but it is safe to assume that the main focal points are in the center).
take this weighted areas (blobs) average them in HSL space and now calculate color temperature - sorry for obvious link but the equations are ok.
This method performs quite good experimentaly, some parameters should be adjusted per type of image, sorry I do not remember exact parameterts (proven to give good results experimentally).

Unfortunately your task must be heavily modified to reflect how people perceive images, how they neglect the color of edges (which give quite big boost RGB-wise). What they focus at and how they remember. By the way, the reception of the image tone is a bit skewed by the represented objects - the attraction makes the tone warmer while repulsion makes it colder.
So please take a look at awesome articles:

Kraft, T. W., Schneeweis, D. M., &amp; Schnapf, J. L. (1993). Visual transduction in human rod photoreceptors. The Journal of Physiology, 464, 747–765.
Ho, H.-N., Iwai, D., Yoshikawa, Y., Watanabe, J., &amp; Nishida, S. (2014). Combining colour and temperature: A blue object is more likely to be judged as warm than a red object. Scientific Reports, 4, 5527. http://doi.org/10.1038/srep05527
Evaluating color texture descriptors under large
variations of controlled lighting conditions