I don't think the ac shuts all the way off, it just goes to a higher temp to conserve energy which is almost as dumb as going off considering Florida is ungodly hot. That being said, AKL had these at my last stay and balloons are not permitted on the grounds. While my room felt stuff after returning from the parks, I never woke up once from being too hot and I mind heat.
I think if the desk told me to use a balloon I would ask if they were paying for it or if this was part of a scam to drive up merchandise sales. If they were providing the balloon, they would be fixing my thermostat.