Yes, shut it off, especially when going away or not listening for over a week. You are just wasting electricity. It only takes about a half hour roughly for most things to fully warm up. Class A may take up to 90 minutes to sound its best.
The only piece of audio equipment that ever came close to starting a fire was a carver receiver I had in the late 1980's, it shot a big flame out the top cover, so I suppose if I would have put a magazine on top of it there might have been a fire.
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