You'll be fine, don't worry. Some people...perhaps your parents...have this thing about unplugging certain appliances, and it doesn't really make sense. Once you've switched off an electric appliance, it's disconnected from the power. (with the exception of some digital controls) Think about it....we don't unplug our electric stoves, televisions, air conditioners, etc when leaving the house. How is a heater any different? As long as you turned it off, you'll be fine.....even if you hadn't turned it off, it would probably be okay. As you pointed out, it has a thermostat to prevent it from running continuously. As long as a pet doesn't knock it over, all it would do is waste a little energy heating the house with nobody there to enjoy it.