"Edwin Pawlowski" writes:

http://www.mge.com/home/saving/thermostat.htm
http://www.energy.iastate.edu/news/p...backtherm.html
A common misconception associated with programmable thermostats is that a
furnace works harder than normal to warm the home back to a comfortable
temperature after the thermostat has been set back, resulting in little or
no savings. Years of research and numerous studies have shown that the fuel
required to reheat a home is roughly equal to the fuel saved as the home
drops to the lower temperature. This will result in fuel savings between the
times the temperature stabilizes at the lower level and the next time heat
is needed. The longer the house remains at the lower temperature, the more
energy saved.

Of course, you need to take into account that this talks about *energy*
used, not cost. If energy costs the same any time of the day, no
matter what the temperature differential (typical for gas or oil heat),
then energy and cost are the same. But there are some systems where
this isn't true. Pure resistive electric heat can cost different
amounts at different times of the day in some locations.

And heat obtained from a heat pump gets a lot more expensive if the
house gets cold enough to bring on the resistance heaters instead of
just running the compressor (that's a case where it actually uses more
energy for the same heat output, since the resistance heater is much
less efficient than the heat pump heat). You may be better off letting
the heat pump run some during the day to keep the house warm enough so
that when the setpoint comes up at 5 PM (or whenever), the resistance
heaters are not used.

So the minimum-cost option can depend on the system type.

Dave