Can I make a container of (kind of) perpetually boiling 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.