Which heating system is the best for Riverdale High School based on what we have learned so far about molecules and temperature? please help

Now, one of the of the common themes in schools with any heating plant is intermittent use. The schools are only in operation for the most part around 8 hours a day (with the exception perhaps of if someone is using the school for some night event but this is an exception). So naturally most school operations departments want to take advantage of night time & weekend set backs to save money on natural gas. They will run the schools to 20 degrees celsius (68 F) during working hours and would to set back as much as possible (typically to 10 degrees Celsius which is around 50 F) to save money due to reduced heat loss, but still protect the school from freezing and provide a reasonable temperature to bring the school back up to temp from on Monday morning.

Explanation: