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There is a mountain of research in the area of the effects of temperature on learning, which all points to the same inescapable conclusion. There are some typical papers and news items below. The first link is to a compelling comparitive case study of a Devon school showing huge savings.
Click above for case study
Excessive Working Temeratures
NAS/UWT Bulletin 2022
Startling statistics regarding learning
Thermal Comfort
Health and Safety Executive
Definitions and causes
Educators, Students Forced to Deal With Sweltering Classrooms
National Education Association (USA) News, 2019... very relevant to the UK now
HKS Working Paper No. RWP18-014
A Paper from Harvard comparing the SATs results of over 10 million students: biggest study ever
In The Green
Leadership Summary, Gareth Marshall, Pied Piper 2021
How Extreme Heat Affects Learning
Stanford University News
Far reaching conclusions on a global scale