Heating is more than the furnace
A heating system has to produce heat safely, transfer that heat effectively and distribute it throughout the home. The thermostat, controls, fuel or electrical supply, heat exchanger or boiler, blower or circulator, ductwork or piping, and venting all play a role.
A furnace can be firing correctly while poor airflow causes comfort problems. A boiler can produce hot water while circulation or distribution problems prevent certain rooms from heating properly.
For that reason, a heating diagnosis should consider the complete system rather than only the heat source.