Here is what is on the table. We know that natural convection does not cool things quickly enough. The hot air pools around the device and slowly rises away from it. Coils are not efficient at convection cooling like a heatsink would be. A fan blowing creates positive pressure. Anything in the path of the airflow creates eddies or pools of air that do not move, and it also redirects the air that does. A fan blows and sucks at the same time. If you utilize the negative pressure or suction, you MUST use a shroud, but by doing this you direct the airflow. The pools of stagnant air are no longer an issue because they can't redirect air.
What does any of that mean? It means just blowing a fan on the voice coil without careful planning will probably not help by any measurable amount. It CAN actually hurt if the cooling that the sub designers built in is obstructed by the airflow you've forced into its environment.
In my opinion, formers built out of high thermally conductive ceramics should be utilized and flat-wound coils could have their shellac sanded away on the side to come into contact with the former (as it is an electrical insulator) Then the ceramic naturally turns into a heat spreader, and inside of it, could be heat pipes. (Hollow channels that contain fluids that evaporate at low temps.)
Then make the dustcaps a lightweight aluminum heatsink. I don't know how much moving mass this would add. It would certainly add to production costs, but it SHOULD up the thermal power handling limits considerably.
Don't forget, the subwoofer moves on its own so the coil is already moving through air. I realize that this air stays basically stagnant and the same heat gets re-introduced to the voice coil, but the fan WILL NOT necessarily break this stagnant air up. It could actually CREATE more stagnant air. It's a great idea, but it will probably fail in implementation.