It was first brought to my attention by a local HVAC Contracting company, that a programmable/setback thermostat would actually cause my home heating system to use more energy, and hence for me to have higher heating bills. Their explanation was that the energy required to increase from 60°F (16°C) to 69°F (21°C), was higher than that to simply maintain 69°F (21°C) over the same time period. According to them, this was especially the case when the outside temperature fell below 20°F (-7°C).
With a little further digging, I found this idea may be specific to heat-pump style systems, as described by The Capital Gazette. This may have led to the misconception that this applies to all heating system types.
The California Energy Commission describes the benefits of "setback thermostats" and mentions this misconception:
It's a common misconception that leaving your heating system on all day is more economical than setting your thermostat back. In truth, leaving the temperature inside your home constant will most likely cost you money.
Your savings can be impressive. Recent studies show that properly using your automatic thermostat should cut your heating costs from 20 to 75 percent. In summer, such devices may shave your cooling costs by 15 to 25 percent. (Your actual savings will depend on such factors as the climate in which you live, the amount of insulation in your house, what temperature you set the thermostat, and the rate structure of your utility company.)
I have looked elsewhere on the 'net and can find only contradicting unsubstantiated claims, most of which do not distinguish the type of heating system.
Is there any research to support the claims of either side? Does it really depend on what type of system is used?