Hello, I just moved into a house built in 1927, with a gas furnace with 4 radiators, two floors, and a cellar. there are in wall air conditioning units in the two bedrooms and the living room. The thermostat is in the living room... ... would the Nest thermostat work well for me? Would it save money over the typical ancient thermostat that is currently installed? Anyone have experience with the Nest in similar conditions? Thanks! r.