The PIII 733 I ordered from eBay arrived today, and I got it up and running tonight. It is a lot faster than its predecessor, the K6-2 machine, although it is a lot noisier.
But, I got the screwdriver and snips out, and removed the fans from the PSU and the CPU, and replaced them with a couple of old fans, an old PSU fan for the CPU, and an old 486 fan for the PSU. I then wired these two fans in series, which slows them down considerably, and makes them an aweful lot quieter.
The heatsink on the PSU is a lot hotter now, but it has been running for some time, and it seems fine. By fine I mean no fire.
The only problem which remains is a BIOS warning. When I disconnected the origonal CPU fan it had 3 pins, black, red and white, but my new fan only has 2, black and red. The white is obviously some kind of monitor to allow the motherboard to panic if the fan stops. So now on startup it tells me there is a fan failure, and press F1 to continue. There is nowhere in the stone age BIOS to configure this alarm, so we may have to live with it.... bit annoying, no remote reboots.....