There are two thermostats, one that controls the heat for upstairs and one fro down stairs. The heat up stairs isn't turning off through the thermostat. Can it be a faulty thermostat?
It could be a faulty thermostat or it's a faulty zone valve or a control unit at the boiler. Zone valves open close to regulate the hot water to the area it's assigned to. The old zone valves would have a relay on the valve that would activate the pump on/off and open the valve to let hot water thorough also. That signal came from the thermostat (but I used to deal with old types back in the 80s I don't know how the new ones operate). Your thermostats may connect directly to some sort of control unit with relays on your boiler only, from there the signals will go to the appropriate zone valves pump(s). You're probably going to need a service man to track down the problem for sure.
you can disconnect the wires to the thermostat and see if that turns the zone valve off if it does change the thermostat if that don't work than time to check the zone vales .we use Weil/McClain and there is 4 zones and 4 thermostats to each boiler , your zone valve might be hanging up , if you have the type of zone valve that has a U shaped metal cap on it take it off and under you will see a round motor with a round cap on it take off the round cap and see if you can with your finger tip spin that counter clock wise and free it up to shut the zone off . they hang up some times you could put a fine oil lightly on it , or buy a new motor for it , if you have the other type of zone valve that twists on than the plunger might of tilted and hung up in the valve you can try pushing down on the manuel over ride lever and unjamming it if that don't work you will need a new power head for it .changing the power heads are easy changing the valve is a pain . good luck