An aquarium heater that is disposed on an outside surface of the aquarium tank for maintaining the water in the tank at a selectable temperature. The heater is preferably supported by a hanger or holder from a top edge of the tank and has a heat transfer plate disposed in intimate contact with a side or back wall of the tank. The heater includes, in addition to the heat transfer plate, a plastic or phenolic housing, a heating element, insulation and a settable thermostat contained in a temperature-sensing section of the housing. When the tank water is below a threshold temperature the thermostat closes coupling power to the heating element, which is preferably a rope-type resistance heater covered by a metal foil blanket, and when the temperature of the water reaches the threshold the thermostat temporarily opens to uncouple power to the heating element.