You have a couple of options here, I think.
One would be to use a BackgroundWorker. This is a common helper for multithreading in applications. It exposes a DoWork event which is handled on a background thread from the Thread Pool and a RunWorkerCompleted event which is invoked back on the main thread when the background thread completes. It also has the benefit of try/catching the code running on the background thread so that an unhandled exception doesn't kill the application.
If you don't want to go that route, you can use the WPF dispatcher object to invoke an action to update the GUI back onto the main thread. Random reference:
http://www.switchonthecode.com/tutorials/working-with-the-wpf-dispatcher
There are many other options around too, but these are the two most common that come to mind.