What I've inferred from various stuff is that aquarium heaters contain a thermostat to monitor the temperature of the water, so its not just blindly heating. Going from the example you gave, if a room started to heat up/cool down and therefore start to raise/lower the temperature of the aquarium, the thermostat in the heater would sense the change and adjust accordingly. Granted, the quality of the thermostat can vary and be inaccurate, so it's important to have a separate thermometer somewhere in the tank to be able to check the temperature and useful to have an adjustable heater.
That said, the heater will cease to heat if the water gets warm enough, but it will not cool the water.
This is just my best guess from reading my heater's instruction manual, so if I'm wrong, someone please correct me
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