I admit that I didn't read the whole thing - just the abstract and skimmed the first couple of pages.
That said, given that they were talking in the first couple of pages about how heat can degrade adult performance on a variety of intellectual tasks, I wonder if they know whether the results had to do with the kids' being too hot - or the teachers. Hypohydration is definitely a potential issue for teachers, too. I remember my mother talking about how she carefully rationed how much she had to drink, because it was so difficult to go to the bathroom during the day at school when she was teaching elementary school. And she was a "specials" teacher, so she probably had more breaks than the average classroom teacher.