The answer to 'why is my air filter not heating' is that your air filter is not designed to heat up. The air filter's primary function is to trap and remove dust, dirt, and other airborne particles from the air flowing through your HVAC system, not to generate heat. If your air filter is not heating, this is normal and expected behavior.
Common causes for an air filter not heating include a properly functioning HVAC system, where the air filter is simply doing its job of filtering the air without any heating or cooling involved. The air itself may feel cool or warm depending on your HVAC system's settings, but the air filter itself should not be generating any heat.