Threading functionality (Native Windows API threads) is available within Showcase, but there is no threading functionality exposed in the API. It is up to you to write and manage threads in your add-ins. The Showcase components that are available in the API are single threaded. When writing UI using wxPython (for example, adding a dialog), make sure you are running in the UI thread.
from RunInUiThread import RunInUiThread RunInUiThread(constant)