I have an older AirPort Express that runs very hot. Is this common for this device?

The rule of thumb for an older Express is that if you cannot hold your hand against the Express for at least 15-20 seconds, then it is running too hot.

If that is the case, give the Express plenty of airspace and keep it away from other nearby electronic devices that may also be generating heat. Unfortunately, not much else that you can do, other than be aware that the Express will likely need replacement in the near future.