First, separate the two kinds of running
Check the thermostat's ordinary user screen. Is its fan setting “Auto,” “On,” or a scheduled circulation mode? Record the setting before changing it. If your owner's instructions allow, choose “Auto” and see whether the existing fan-only operation settles normally. Do not change installer settings or disconnect wires.
Notice whether the room reached its target before the heat stopped, and whether air from the vents gradually cooled. Those details help distinguish an ordinary end-of-cycle delay from heating that stopped early while the fan kept going.
A safety shutdown is another possibility. Carrier explains that a high-temperature limit can stop the burners while the blower continues cooling the equipment. That is a protective response, not proof the switch itself is defective. Carrier cold-air guidance.
What can you safely check?
With the equipment off and only at a normal homeowner-accessible location, check the filter according to the owner manual. Note its size, type, and condition. Keep return openings and room registers clear of furniture. Do not reach inside the furnace, press a limit reset, remove a fan control, or turn adjustment dials found behind a panel.
Keep the repair question focused
We recommend asking the technician to identify what is telling the fan to run. Older equipment can use a different fan-control arrangement from newer furnaces. The useful finding is which control or condition explains this furnace's behavior, not which component is common in an internet video.
Ask for the expected delay for your model, whether heat is ending normally, and whether a protective control is opening. If a control is blamed, ask what test shows it is failing and whether overheating or restricted airflow was also checked.
A repair may be sensible when a specific fault can be corrected and the rest of the furnace's condition supports continued use. Replacement deserves a wider comparison if the inspection finds other material problems or a needed part is unavailable. Age helps plan that discussion. It does not diagnose the running fan.
The next step is to share the fan setting, approximate run time after heat ends, and whether the home reached its target. Ask for a diagnosis of the fan behavior before approving a larger project.