Think about how you could adjust the operation of your machine if you temporarily assumed it were not a closed system:
You could speed up the operation of your machine by heating the water and/or cooling the ceiling. In that case your machine is a typical heat engine, with energy being transferred from the hot water to the cold ceiling by convection and the spinning of the turbine a side-effect.
You could slow down, or stop, your machine by cooling the water and/or heating the ceiling. That's how the rear-window defroster on your car works, after all.
That means that somewhere between those two temperature gradients is a configuration where your machine doesn't run at all. If you set it up and leave it closed, it will eventually reach this equilibrium configuration and stop.
Now it is possible that, since gravity is involved, the equilibrium configuration isn't actually at uniform temperature. For instance, if the chamber were ten miles high, the water vapor molecules near the ceiling would have less average kinetic energy than those near the bottom, and a lower effective temperature. But, like all perpetual motion proposalslike all perpetual motion proposals, it will only run for a while at best.