Has the heater just an electric coil in a metal case, with no fan? Sometimes electricity can have a vibration of it's own, and you may have a hard time detecting it. The vibration is caused by the electricity itself.... IF the knob is very easy to turn... something you could turn very easily with one finger by just touching it. ('AC', or 'alternating current', as household electricity is called, actually changes it's direction in the wires 60 times per second, and it might be able to move the setting via the vibration this causes.). However, if the knob is stiff enough to turn that you have to take hold of it and grip it to turn it, I would guess that it isn't the vibration of the electricity that is changing the setting, but more likely a little ghostie.
The picture is really the thing that leads me to believe that it might be a ghost, because the heater probably isn't touching the wall, and causing vibration enough to move a picture on another wall away from the heater would be next to impossible. That is my thought, anyway.
The story about the sheltie is very intriguing!!
I'll bet it was something meaningful in some way. It is amazing that even with sealer and paint, it kept coming back. Your dad must have been ready to pull his hair out!! LOL
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