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One of the things which seems to be missing in the experiment is the presence of other masses which absorb and release thermal energy (like pieces of furniture, carpet, etc.) It would be interesting for you to add a block of wood and a rock and maybe a piece of metal to the beakers and run the experiment. Homes and office buildings are not empty boxes, but contain masses which absorb and release non-instantaneously and at different rates. If you are trying to cool a house with lots of furniture, you have to cool the furniture as well as the air. This fact might contribute, sub-consciously, to the student's perception of which cycle is better.
Bill Nettles