One more thing (ya, there is always at least one more thing...)
Are you sure there isn't something confudling the thermostat? It might be working correctly for the cubic foot or so of house around the thermostat but that might be a poor representation of the rest of the house. Sun on the thermostat will definitely make it read incorrectly for the rest of the house. A vent that blows directly at the thermostat will also make it behave poorly. A downstairs thermostat won't do a good job of keeping the upstairs cool in the summer, or the downstairs warm in the winter without cooking everyone upstairs.
And, there is always the "pop the cover off and look for a calibration screw" approach
When our friend Phil put in the new furnace and central air the guy was amazing. He used a simple hand held pyrometer and ran the system over and over again over a few days. Our cold air return was a disaster as were the ducts etc, so it was all replaced. The guy actually used ducts with levers in them and balanced everything. On a hot summer day if we set the thermostat for 74 this old house is pretty much 74 from the upstairs to downstairs. The guy tweaked and peaked everything. On a cold winter day if we set the thermostat for 70 it pretty much maintains 70 throughout the house and this place is old.
I work a lot with temperature but home heating and air conditioning isn't my forte. I do know you want the thermostat in a large room and you don't want it near a duct blowing on it obviously or where direct sun through a window will be hitting it. I am OK with the common sense stuff. I now, after watching Phil, have a better understanding of controlling air flow to balance heating and cooling.
The suspect t'stat in question is in the lower floor with it’s own heating/cooling system – a heat pump. (Our house in on a steep slope so part of the lower floor is actually a basement). Now we have a stair well between the basement and ground floor (upper level) where we have another independent system with its own t’stat. There are doors at the top and bottom of the stairwell but they must be left open during the day for the cat to go down for his “toilette”. This means I must keep the basement system at a set point that keeps the temp slightly lower than the temp on the ground floor so warm air won’t migrate up the stairwell and cause the upper unit to run excessively. Although I would like to maintain the temp on both floors exactly the same it’s hard to know what the set point in the basement should be. Empirically I run it at 78 which gives me a presumed real temp of 75 (averaged between the grouping of three thermometers) while the upper floor t’stat is set at 76 and, after a few cycles of running, settles on a displayed temp of 76.
Geez, I wonder how you model a suitable control system based on multiple floors, each with its own temp control with vertical draftways like stairwells
