The answer to 'air filter not heating' is that a clogged or dirty air filter is the most common cause. When the air filter becomes too dirty, it restricts airflow through the HVAC system, which can prevent the furnace from heating properly. This can lead to the air filter not feeling warm, even when the furnace is running.
Some other potential causes include issues with the furnace itself, such as a malfunctioning thermostat, igniter, or blower motor. In some cases, a problem with the ductwork or air vents can also restrict airflow and prevent the air filter from heating up.