First let me say this - I have a strong background in physical science and applied my full "facilities" to solving such a problem when I did maintenance in an OLD apartment house.
Thermostats are the "brain" of a heating/cooling system, but unfortunately are WAY too often misused, misapplied, or improperly installed.
HVAC systems (like airplanes) are (1) designed by people with PH'Ds, (2) built by people with Masters, (3) Installed by people with MAYBE some college, and finally (4) serviced by HS dropouts!
Each type of system and installation will have peculiar installation problems which the installer must REALLY be knowledgable concerning.
Without complete info on your system - short of paying for the BEST HVAC consultant in your area to come out and look at your problem (which is ALWAYS a good idea!), keep experimenting with your programmable. If it does not do the trick for you (and they only work right when PROPERLY installed for a HVAC setup they are designed for) then go back to the (so-called) old fashioned bi-metal (get a new one) type (Honeywell, etc.) They are
reliable and accurate EXCEPT for one small problem and that is the "anticipator" (which I personaly think was and is a design mistake) as Timskitties mentioned (sounds like TK will know what I'm "tacking aboot" - Hi TK!
). Anticipators need to be properly "set" (or disabled IMO!).
Bottom line is... unless you have a modern system installed in a quality built (insulated) house/apt, etc. by a QUALIFIED installer it becomes increasingly difficult to get a properly functioning system the further away from this criteria you get.
If you need more help, I'm here, but need specifics on what type the HVAC system is and the house its in.
Gotta go...Fluffy's hungry!!!