Every now and then you can find NOS 'Arctic Cooling Copper Silent 3' (sometimes 'Copper Lite') coolers.
It needs a bit more space around the socket and the retention clip may have to be modified from 3 point to two point but it's silent and more than enough for any PIII plus mounting pressure can be adjusted with a screw and you can open the top to oil the bearing.

Getting a big and quiet cooler is one option, but finding a halfway decent Socket 370/A cooler now can be difficult, thanks for the pointer Doornkat 😀

My preferred solution is to add in a temperature controller, this and a slower/bigger fan makes the system much more tolerable:

Ebay Link for the cheapest one I can find
Just search for a "Denoised" fan controller. There's a little bit of setup required to get the base temp and fan curve set, but doing it this way also means it works in DOS.

Antec made a pretty nice and not loud one. I bought a few a while back because they are of thin-fin design and work very well.

There are a few on eBay right now. Just search for:
Antec 370 cooler

If you want to reduce the fan speed, you can either get a temp controller or a manual controller.

The Antec cooler is also a good suggestion since it's avaliable. Is it compatible with the thick Tualatin heatspreader?

Doornkaat wrote:

The Antec cooler is also a good suggestion since it's avaliable. Is it compatible with the thick Tualatin heatspreader?

Should be as I have also used them on Socket 7 systems with K6-2 CPUs. If the bracket seems a little too tight, you can always bend it a bit to make it not so tight.

I use a startech cooler. When it runs in full power it is very noisy. So I build in a silent adapter from noctua. It reduces voltage so the ventilator does less speed. Temperature seem to be okay - even after playing several hours. And the noise is really low now.