Just a little more thoughts on the lighting / heat issue.
Infrared light heats up surfaces that it hits. So it impacts leaf surface temperatures greatly. LED generally lacks infrared spectrum and therefore the environment must be run warmer to get the leaf surface temperatures up to optimal.
HPS has more infrared than CMH and thats probably a big part of why people say CMH runs cooler than HPS.
When dealing with totally different lamps like CMH and HPS there is an inherent difference in the percentage of input power that is converted to heat in the arc tube. Some percentage of energy is converted into light and some into heat. A CMH is more efficient and more of the energy is converted into light when compared to the HPS. So combine those two factors, infrared and efficiency you can easily explain why people observe CMH running cooler than HPS watt for watt.