To control light temperature, most simple solutions consists in defining the wanted temperature as a function of time while in fact, sun temperature depends on the air mass, the position of the sun and the position on Earth.
By calculating the sun temperature, one may directly get the accurate temperature to control lights from sunrise to sunset (whatever the season, local change of hours, etc. ) with the correct value (ie, depending on seasons, the maxium temperature is not the same).
For european people, we can estimage this temperature with [1], but for a “good” estimation, one may calculate the perceived spectrum at a given position and elevation (ie, calculate what is absorbed in the atmosphere, in the visibale range), and then deduce the accurate temperature.
[1] Koppel, T. (2012). Dynamic Lighting System for Workplaces at Northern Latitudes. Safety of Technogenic Environment, 3, 39-44.