Why will the central heating unit continue to run after reaching the set temperature? It does not read that it is reaching a higher temperature, it just continues to run at the reached temperature set.
If this is a forced air system, the blower will continue to run for a specific amount of time after the unit stops producing heat. The unit will no longer be producing heat, but the blower will continue to run to spread the heat that was produced when the unit was full on. If it didn't, a lot of the heat produced would be wasted.
Some units use a heat detection circuit to determine when the blower should turn off. Most however, simply keep the blower on for a predetermined amount of time.
There are also a set of switches in the unit that relay the thermostat demands to the unit. They control how long the blower runs after reaching the desired temp. Most units run for a set amount of time after reaching desired temp. In time, though, those switches (that look like little pieces of aluminum foil) will wear out and cause the unit to run for long periods of time because they won't tell the blower to turn off.
I suggest timing your unit. If it keeps running after the thermostat clicks off for more than 5 minutes then you would need to get the unit checked out. There is also a possibility it could be the thermostat, but that is not as likely.
Electronic thermostats will only display whole degrees, but most (this varies from one manufacturer to the next) will measure fractions of a degree and switch the relay that controls the HVAC perhaps after it reaches 72.5 for example if the target is 72 (in heat mode). They may also vary in the target temperature in cool mode vs. heat mode. The underlying explanation is that the electronic components are measuring fractions of a degree but only displaying whole degrees and operating according to the underlying programming that is opaque to the user unfortunately.
Thermostats have a temperature range around the target temperature. If you set it to 72, it may have a 2 degree range allowing the temperature to fluctuate from 71 to 73. Without this, the hvac would be constantly cycling on and off, shortening the life of the hvac and reducing your energy efficiency. On some thermostats, the range is adjustable.
It's like inertia, but with heat; just like a motor spins down after the power is off, furnaces still have some heat in them after the flame is shut down.
Thermostats have a feature called an
anticipator. It will shut down the furnace when the ambient temperature gets close to the desired settings. The system will then run the fan for the remainder of the cycle as the accumulated heat will be dissipated in the air flow.