How to tell if thermostat is bad

Even though its on an inside wall, still could be a draft in the wall. As they had to drill a hole in the plate to get the thermostat wire up to the thermostat.

Could just be the thermostat isn't accurate.

Some thermostats can be offset to match the house temp, check your owners manual.

Not all drafts are cold air drafts.

Could even be a supply run to the upper floor is in that stud bay.