Typically you pass parameters to the Thread. Run the logic in the background. And then post back any modifications you need to do to any of those objects, or UI elements on the UI thread using SwingUtilities.invokeLater(). Typically I create a simple a utility that allows me to specify what should run on the background thread, and what should run on the UI thread. SwingWorker is something you could use although I find it extremely painful to use. Something simple like this:
new AsyncThread<Param,T>() {
public T executeInBackground( Param param ) {
// do something long running
T result = // do something long running;
return T;
}
public void executeOnUI( T result ) {
// update the UI here, or modify the model, etc.
}
}.execute( param );
AsyncThread would execute the executeInBackground() method on another thread. Then internally it would post back to UI thread using SwingUtilities.invokeLater(). Then executeOnUI would run on the UI thread. The execute() method could create a thread to run in background, handle exceptions, etc.
I'd let the GUI possibly kick off the thread, and let the GUI pass it's model, or whatever part it needs, to the thread. Instead of the other way around. That way you can have the UI give feedback about that background thread that's running. But, you can't let the background thread touch (write/modify/change) members of that model that the UI thread would be reading/writing too at the same time. So if you plan on modifying the model in response to the background thread, post it back to the UI thread to be safe.