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Hi atleastsixcharacters,
welcome to the Sony User Community Forum..
Not a dumb question I have a similar issue with a decoder box, looking at the manual there is reference to your device automatically switching to Power Saving Mode, so I wondered does the fan still sound when your device is in power saving mode??
To answer your question from what I can tell there is only the on/standby button, so switching of at the plug would be the only option to stop power reaching the fan, etc..