Classroom Temperature Gradient

Yesterday, in my microbiology class, I became mindful of the temperature gradient in the room. I noticed that when I sat higher in the classroom that the ambient temperature was higher than when I sat lower in the classroom. My microbiology class is taught in a large auditorium and there is a 20-30 ft. difference in elevation from the front row of the class to the back row of the class. The fact that air density is affected by temperature causes the hotter air to rise and the cooler air to settle at the bottom of the classroom.