Yes, but no.
The RPi needs to boot, during which time the fan is uncontrolled.
You would need a large amount of other components to drive the fan, sense temperatures etc. Even with a Gertboard you would have to design and build the sensors.
It's over-powered. It could regulate the temperature to within 1 degree, but why, in view of point 1, would you want to?
Hidden away in the PC case, nobody gets to see how clever you are, so it isn't any good even as an ego thing.
It would cost over £50, maybe over £100.
Since you have to build some electronics anyway, using a microcontroller like a small PIC or and AVR would be almost as easy to design and would produce a better result.
It is a valid project, using the RPi will work, but I think with a little more thought you could come up with something that is a better fit to the capabilities of the board.