I have a NOMA thermostat (model 52-2558-8). After reaching the programmed temperature, the furnace stays on without shutting down (8 degrees before I manually shut it off). Is this a thermostat issue or a furnace problem?

Does it shut itself off at or after the 8 degrees,, try setting the programmed setting 8 degrees less, see what happens

Check the wiring between the thermostat and the furnace. Both ends. That is the most common source of that type of problem. Maybe someone didn't follow common color codes, or terminals are not designated the same, or the furnace control is bad, or... Lots of things to check. Just eliminate one at a time.

EPM

Turn off furnace. Remove the W thermostat wire at the furnace. Turn on power. Furnace should stay off.