Say we extend this to the limit. What if we cooled the cold balloon to the point were the gas inside it is the same pressure as the atmosphere. You hook up the little turbine and you measure zero energy.
So hot balloon produces X Joules of energy, cold balloon produces zero Joules of energy. A third baloon with same mass of air etc. somewhere between the hot and cold balloon temperatures would be Y joules of energy.
So from this, I think it is safe to say that X is greater than Y is greater than 0.

