Calling a method when thread terminates

The BackgroundWorker class exists for this sort of thread management to save you having to roll your own; it offers a RunWorkerCompleted event which you can just listen for.

Edit to make it call a helper method so it's cleaner.

thread = new Thread(() => { Synchronize(); OnWorkComplete(); });

...

private void OnWorkComplete()
{
    Close();
}

If you have a look at a BackgroundWorker, there is a RunWorkerCompleted event that is called when the worker completes.

For more info on BackgroundWorkers Click Here

Or

You could add a call to a complete function from the Thread once it has finished, and invoke it.

void Synchronize()
{
    //DoWork();
    //FinishedWork();
}

void FinishedWork()
{
if (InvokeRequired == true)
  {
  //Invoke
  }
else
  {
  //Close
  }
}