I'd just make a small change to the very detailed answer Chris gave; I would set myThread to be a Daemon thread by myThread.setDaemon(true); which will basically keep the thread active as long as you have other non-Daemon threads working which need your background thread around. When all these threads finish then your Daemon thread is stopped by the JVM and you do not need to handle it youself in contextDestroyed.
But that's just my 2 cents.