I use “Beelink” brand mini PCs for this purpose. (They are the same form factor as your photo.) I have three, and they’re all good. I’ve used multiple distros on them with no compatibility issues, but MX Linux is my daily driver.

They have fans built in, but the cases on the higher end ones are metal, which helps with heat dissipation. The only downside with that is that sometimes USB peripherals get super hot while plugged in, and I had a mouse dongle that would overheat and malfunction. A simple USB hub fixed this problem (the hub itself apparently didn’t mind getting hot).

I use a “Mini Keyboard with touchpad” on the ones connected to TVs. I recommend those as well. Rii brand is decent.