A. If you use a 5 degree setback you can save between 5-10% on your annual cost to run the furnace.  The cost to install a programmable varies greatly depending on what you purchase. It may take between 5-10 years or more to get a full payback. 

A. Programmable thermostats can save you money if you use them properly. Typically with a gas furnace if you program in a setback of 5 degrees when you are at work and while you are sleeping you will use less energy in the month.  With a Heat Pump you would need a special thermostat that would not bring on the electric backup heat when coming out of setback or you would use what you just saved to get the house back to temperature. In summer, avoid increasing the temperature for work and sleep times during extreme weather because the AC will take a long time to get back to your ideal comfort conditions.