Can I make a container of (kind of) perpetually boiling water? It's a common school experiment to make water boil at room temperature by putting it in a container and reducing pressure. 

I am wondering if it is possible to make a sealed sphere containing water where the pressure is carefully set to room temperature so that it boils "forever".

Obviously it can't boil forever, because it would eventually all turn to vapor. What I am thinking though is that minor fluctuations in room temperature will cause it to cycle between boiling and condensation without the need for any power.

Is this line of thinking correct? Has anyone attempted to make something like this? I think it would be a really cool desk ornament, like a little box of cycling boil-condense water.
You can buy a hand-heat powered boiler. But something must provide energy to keep the bubbles forming, and remove it to condense the gas back to liquid, or it would all be in the vapor state. In this toy, the heat of your palm provides the input energy, and ambient air cools the vapor in a condenser.

BTW, this demo won't work if the room temperature is exceedingly high, because the liquid (probably an ethanol-water mix) won't condense and the vapor pressure becomes too high for bubbles to form in the remaining liquid.