Most don't require cooling, but will have better clocks. The 4 itself throttles under heat (above 60C and heavily over 80C), and seems to have good enough behavior even if not actively cooled.

Probably either the Odroid N2 or HC2 or Nano Pi M4.

The one feature all these boards have in common is their CPU is mounted on the _bottom_ of the board, allowing a much larger heat sink to be mounted without obstructing anything. The lack of this feature in on the RPi 4 is a fatal blunder IMHO and why I chose not to buy it.

I currently use a Nano Pi M4 as my main desktop computer. It has no active cooling, only a big heatsink which covers the entire rear of the board. As I write this, I have three browser windows open containing a total of 30 tabs while streaming a 44 kHz stereo 128 kbps audio stream. Its CPU temp is holding at 32 C.

Even Pi 4 B doesn't seem to require active cooling. It will do fine-ish (sitting at barely under the temperature cutoff limit of the thermal throttling, under load, by using a bigger type of passive heatsink), which is still quite a feat. To have a cheap totally silent computer with the specs that 4 B provides is still a great achievement.

Raspberry Pi 2 wasn't a beast, but mine runs cool enough in a 22'C room to max out at 62'C when I run an ffmpeg transcode.

Someone else graphed out the 2,3 and 4 temps under idle and load at 22'C:

https://www.reddit.com/r/raspberry_pi/comments/dspb5g/temper...

My Pi 2 stays comfortably cool, but it's rarely under heavy load. It serves as a Gopher file server for a bunch of old computers and occasionally a music player, so I think the heaviest thing it does at any time is to decode mp3/ogg.