I am renting a house which has a Trane heat pump

I am renting a house in NC which has a Trane heat pump XL 1200, Model# TWX72AA100A1, Mfg. Date of 01/88; and a fairly new Honeywell digital thermostat.

During the cooling season the unit ran fine. Now that it has been switched to standard heat mode, the unit runs continuously for hours even after room temperature has been reached. It then brings the temperature down and it heats again like it is in a loop and the unit never gets a signal to turn off. It then has to be shut off manually at the thermostat by lowering the set temperature. However, it works just fine in emergency heat mode and shuts off when set temperature has been reached.

Would that problem indicate a faulty thermostat calibration or a potential problem with the unit itself? The unit is now almost 22 years old, but it has had new parts installed in the past few years. Thanks.