No, they come on when you plug them in and turn off when you unplug them. They MIGHT have something to turn them off if they get out of the water and get hot enough to start a fire, but I wouldn't count on it.
Well, let's figure out how to put a thermostat on it, sell it, and become millionaires!
Keeping the scalding temp right was the most aggravating thing.
It would be easy enough to do that. They make thermostats you can plug things into. Just put the probe in the water, set the temp, plug the heater in, and it will essentially plug and unplug the heater as needed. Would be best to have something stiring the water to provide even heating and an insulated water container to slow the temp fluxuations