There are two major issues with using wood for a PC case. The first issue is heat. The second issue is vibration.
Heat can become a problem because a wood case is not going to transfer heat from the inside of the case to the outside in the same way as a metal case. It is not entirely inaccurate to think of a metal case as a kind of heatsink. The metal is thin and transfers heat well. Heat inside the case transfers easily into the room. Wood does not have this characteristic. Airflow is therefore critical. Make sure that there is an exhaust fan for both the GPU and CPU, and make sure that intake fans provide proper airflow over the hard drives.
Vibration can be an even trickier problem. Wood tends to resonate, which means that a vibration can cause very annoying sounds. Dealing with vibration requires that parts which vibrate be isolated from the case in some way. This includes the optical drives, hard drive, and all fans. One way is to rip out the internals of a case with good vibration isolating qualities and mount those components into the wooden case. A custom approach is to use rubber spacers in areas where components are being screwed into wood. Foam can be packed around fans. Rubber strips, like those used around windows to plug drafts, are also extremely handy. They can be placed around components. If you're very precise, you can glue them to a fan and then slip the fan into a precisely cut fan mount, mounting the fans without any screws at all. Be careful with the glue, however, as many types of glue react badly with rubber.