Be sure to read also my follow-up post, which corrects some important errors. Well, I have tightened up my estimates and gotten within a factor of 3 or so. Since I have had some responses requesting more information I post this whole analysis. It is lengthy, but as a bonus we get a model accurate enough to show why, for example, it does pay to turn off the furnace when not at home. We have been doing some construction lately so I am using data that's a couple of years old, when the situation was more stable.
Heat is forced air heated by natural gas, no humidity control.
There were no other gas appliances at the time. The house is far from airtight and had no reflective coating insulation, but there was a reasonably good blown-in cellulose insulation throughout. Actual heat loss. This is fairly easy. The gas company reports, monthly, both cubic feet of gas consumed and degree-days suffered.