I like the idea of a seperate fan PS, and have considered it myself. I know of the relay, but is there a time-delay type of relay. Like something that would run the fans for a couple of minutes after the system shuts down? ...or would that require some more complicated circuitry?
Per Char Broiled you can use a 555 timer chip and screw with a few circuits. Personally I like and use the 555 in a number of applications but was never a big fan of it for what you want to do.
What you are looking at is commonly called a "Delay on Break" or "Delay Off" as well as a few other names. I like the 555 more in the delay on make or delay on than a delay off circuit.
Personally, quick & dirty as well as cheap I would use something like this:
Any simple relay will work just fine. The circuit would work well using a 12 Volt coil relay. The power comes from a source other than the PC (obvious reasons). You can screw with the values of the capacitor and the resistor looking for a suitable delay. Increasing the capacitor will increase the on time after power is removed using the switch. We charge a capacitor and the relay is held closed. When we open the switch the relay is held closed through a charge on the cap. The cap will slowly discharge through the transistor. When the cap discharges to a point it can't keep the relay closed the relay opens.
Quick and Simple.