A chimney works because hot air is less dense than cold air. A tall, well-insulated chimney can provide quite a bit of natural draft. A six-foot length of plastic pipe attached to the top vent of your case would improve its passive cooling capability significantly.
A PC has a much lower temperature delta than a chimney which seems like it would reduce the potential for an upward draft?
Air at 25 °C with a dewpoint of 7½ °C at one atmosphere of pressure has a density of 1.1793 kg/m3
Air at 40 °C at the same conditions has a density of 1.1228 kg/m3
Air at 60 °C at the same conditions has a density of 1.0554 kg/m3
For a two meter tall chimney, the difference between 60 °C air and 25 °C air adds up to 2x(1.1793-1.0554) = 0.2478 kg/m² difference in pressure. A sheet of writing paper is about 3½ times as heavy as that. Your PC's case is only about half a meter tall and the heat generating components may be near the middle or top instead of being located at the bottom.
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