I'd pay as much attention to humidity as temp.
There's a useful dew point calculator here that will help you see when corrosion / mechanical damage is problematic:
http://www.dpcalc.org/
Then just get cheap hygrometers to put in each room. I actually have a remote sensor not only under my house but in my attic (the sensor is mounted in the attic but the readout is in my office one floor down), because I don't go up there much and there certainly isn't anything delicate like electronics but I want to be informed if there's a problem. This time of year its bitter cold and dry, so I actually have whole house humidifier making sure it never drops below 35%. In regular rooms in the house, of course the HVAC system itself takes care of everything.