I start and stop recording all day. Paint a bit, wait for the paint to dry using a hair dryer, paint some more. When I leave the camera and monitor on, I can study what I've done from across the room on the monitor view. The camcorder doesn't seem to be particularly hot. I'm not sure how hard it is working when it is not filming.
On the other hand, lots of gears and things whirl every time I turn it off, then on again.
I'm not sure which would harm the camcorder faster. I don't worry about leaving the monitor on.