Not a good idea, anything that restricts airflow is likely to cause overheating, your idea of some sort of filtering for a device that has been designed not to have such a filter will reduce airflow to the detriment of the computer.
One more point, a computer should be located above floor level, not just to reduce animal hair but also household dust ingress. Dust tends to settle on the floor and placing a computer that has air sucked into it for cooling purposes will also cause dust to be sucked in.
|