Earlier quoted context omitted.
Your theoretical analysis misses an important physical fact: houses are able to exchange air with the outside world, not just heat. As you heat a normal room, it will expel air in order to maintain constant pressure, and similarly, as you allow a room to cool, outside air will enter again to keep the pressure constant. There was an article about this in the American Journal of Physics [1, 2] a couple years back, and…
This effect isn't going to be very significant. A constant exchange of air will have a significant effect, but a one-off exchange of 10% of the air will be negligible. The reason for this is that the air has a very small thermal mass compared to the building structure. I've got mote sensors in every room in my house, including the hall. When my kids leave the front door open in winter for a few minutes, as kids tend…
Thermal density (specific heat) of air is going to be ~1000x less than that of solid objects.
The specific heat of gypsum (the primary constituent of drywall) is 1.09 kJ/kg.K
For dry air it's 1.0 kJ/kg.K
Air's density is 1.225 kg/m3.
A 6m x 9m x 2.3m (20' x 30' x 7.5') room has a volume of about 130m^3, so a 10% exchange would be 13m^3, or 16kg.
That's about 15 kJ of heat energy per degree C, or roughly 0.0004 liter (0.0001 gallon) of heating oil equivalent.
The drywall would be (in feet) 20x7.5x2 + 30x7.5x2 + 20x30 ft^2 (I'll assume the floor is some perfect insulator for now, and that the room has no doorways), and 1/2 inch thick, or 1.6 m^3. That's about 3600 kg of gypsum, which has a heat capacity of about 4000 kJ per degree C, or about 0.1 liter (0.027 gallons) of heating oil equivalent.
If I'm doing my maths right.
Sources:
Specific heat of gypsum: http://www.engineeringtoolbox.com/specific-heat-solids-d_154...
Specific heat of dry air: http://www.engineeringtoolbox.com/air-specific-heat-capacity...
Density of gypsum: https://en.wikipedia.org/wiki/Gypsum