Many people overlook used thin clients, many of them powerful enough to be a media box and can be had for around $30-$40, and quite a few of them are fanless, heck even ones with a fan in them are pretty darn quiet. And most thin clients will run whatever OS you want on them (full blown windows install, or a flavor of Linux).
I bought a HP t620 plus (which has a AMD Gx-420ca quad core 2ghz) which does have a fan (I got lucky and scored it for $40), installed a GT 1030 ddr5, with 8GB ram, 1tb SSD, 1TB external USB and taxed it for hours and it remained whisper quiet. They seem to fetch around $100 now since a few YouTube channels had videos about them. Stock they don't do YouTube quite well (which is why I installed a GT 1030 in it), and thanks to the GT 1030 it'll also playback 4k60 videos.
I use it for listening and watching music and video, and lite gaming. At full load it only consumes around 40w-50w in total with everything installed.