Okay, I will try to provide as much information as possible.
I am using the Elite mini submersible aquarium heater (25W), by Hagen. It is this model http://ca-en.hagen.com/Aquatic/Heating/Heaters/A748
The item number is A748.
By turn on/off, I don't mean actually cutting power from the heater. It is always plugged in so in a sense it is always "on". Maybe I have haven't been paying attention enough to see it come on when the temperature drops? I'm not sure. It definitely turns itself off, so I guess I don't have to worry about the tank getting too warm for the little guy.
Reading some reviews on Amazon *seem* to indicate that it does self-regulate...maybe someone here with the same model can verify. I've been at home all day and so far it's been staying at a good 80F...I just don't understand how it knows what temperature to turn off at; there is no way to program in 80F or anything..
I will keep checking it out every few hours.