I would be much more worried about the condensation on the peripherals and computer.  In an unheated room during the winter there will be a lot of moisture as things start heating up.  Personally, I would not recommend it, or else put a decent electric heater near the computer.

>I want to relocate a home computer to an unheated sunroom.  It's a Gateway
>200 HMz tower (plus 17 inch CRT monitor, Canon inkjet printer, keyboard and
>mouse).  The system spec says the lower temperature limit is 10 deg C, or 50
>deg F, which is well above our winter temperatures!  If necessary the tower
>could be within the heated portion of our home, with wires passing through
>the wall.  Will the monitor and printer survive and operate at the low
>temperatures, say 10 to 20 deg F, of the sunroom?  Would a black laser
>printer (to avoid ink freezing) be useable?.
>
>

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