When looking at a LIFX Mini Colour bulb via Home by Matthias Hochgatterer, it seems that the only settings provided to HomeKit are Brightness/Hue/Saturation. When I emailed Matthias to ask, he told me to ask the LIFX development or support team to add a colour temperature characteristic for HomeKit.
So, could you please do that? Or is there another way to set temperature?,
Edited to specific about the bulb in question, i.e. a LIFX Mini Colour.