Saying on the classroom situation, movement helps mitigate the effects of blood pooling in the limbs. That's how movement comes into play. Perhaps the same temperature would not impact test scores if the students were taught to make counter maneuvers or had under desk steppers or something else which would use muscle pump action to improve circulation. So my question is if heat alone is affecting test scores or if heat + inactivity is affecting test scores. Installing air conditioning is an expensive solution, but permitting and encouraging movement breaks is free. If movement mitigates the academic impact of heat, then adding movement to classrooms would be a free intervention for low-revenue districts.

As far as bigger picture, a serious global effort to reduce human consumption and soil fuel use seems to be in order. The temperature is only going up from human activity. The more we air condition (and other energy consuming comfort necessities) the faster that planet heats up.