On 2008-01-22, Doug Miller wrote:

Won't be much higher -- heat transfer rate is proportional to
absolute temperature. 70F = 294K; 80F = 299.6K; so the difference
between heat transfer rate at 70F and 80F is less than two percent.

Umm, my understanding is that for convection and conduction, heat
transfer rate is proportional to the temperature difference. So there
is a big change in heat transfer rate for 70F versus 80F air.
[E.g. for 60F building materials, the temperature difference is double
with 80F versus 70F air.]

Look at the original question this way--you want to get the average
temperature of a building from 70F to 50F. Based on all the different
materials and their heat capacities, this will require some number of
BTUs; based on the furnace output rate the furnace will have to run
some number of hours to put out the required heat. Say 2 hours.

Air temperature will be a leading indicator of average building
temperature. So if you set your thermostat to 70, the furnace will
run less than two hours, then it will cycle on and off for a while as
the building catches up to the air temperature, until the total
running time reaches two hours. Or you could set the thermostat
artificially high for two hours and then reset it to 70 degrees. The
two hours of furnace time required occurs all at once.

Clearly the latter strategy causes the building to reach equilibrium
sooner. That's all I'm claiming, not that it is a good idea, will be
more comfortable for the occupants, or that it is more efficient.

Cheers, Wayne