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any kind of closed cupboard is going to be a bad idea
To some degree, any room is a closed cupboard. You can use standard room heating calculations to determine the temperature rise for a given power dissipation.
If you install grilles towards the top and bottom of the door, your server becomes the heating element in a convection heater, and you can generate a fair bit of air flow without mechanical ventilation
Is there any easy way to work out what heat will be generated by a PC?
I have a convenient spot for my new server but it's in a cupboard with limited airflow and I don't want the fans going full blast. I suspect the two aren't really compatible but wondering if there was a way to actually tell.