final JWindow messagebox = new JWindow();
.... 
final ActionListener  action = new ActionListener(){
    public void actionPerformed(ActionEvent e){
        messagebox.dispose();
    }    
};
final Timer timer = new Timer(TimeUnit.MINUTES.toMillis(3),action);
timer.setRepeat(false);
messagebox.addWindowListener(new WindowAdapter(){
    public void windowOpened(WindowEvent e){
        timer.start();
    }
});

------解决方案--------------------
InternalFrame是可以嵌套的内部窗体