With no air at all coming out . i am left with the question , are you sure its the heater fan thats coming on ?
i would suggest that you take your car to a garage and ask them to identify the noise and possible cause. this would at least will take away the guess work and they could quote you for any repair if need.
as it is im left wondering if your car is a turbo, petrol or diesel , if the window is open or closed when hearing this sound, stood or moving.
you seem to think the noise from the interior of the car
behind the dashboard. However with the windows shut and the car moving the noise could easily be coming from the engine compartment and mearly sounds like it is behind dash.
better to get it identified than continue guessing.
Most small garages will take a few minuets to answer this question in the hope of recieving the job to repair it.