I picked up this kit last summer to use with an always-on Plex server: https://www.amazon.com/gp/product/B07CDDGVK7/

I can't hear the fan spinning unless I put my ear right up to it. Never had an overheat-warning, even in the warmer months.

I get what you're saying concerning playing PS1 games on the Pi. The only time my Pi ever got overheated (showing the thermometer icon) was after playing a rather lengthy session of "Crash Team Racing". This case, or one like it, should do you just fine.