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As you can see here, thumbnails are now stored locally with Embedded Media Field. This opens the way to ImageCache integration and more.
This example also makes use of a new formatter, which uses jQuery to replace the thumbnail with an inline video, so that cookies aren't sent to the provider unless the user clicks to play.
Both of these features are available with all of the providers. Although not all providers currently offer an API for their thumbnails; however, in those cases, you can continue to use your own custom thumbnails. To use the first feature, local thumbnails, you'll need to enable Embedded Media Thumbnail, which is packaged with the module. The new formatter is available in any case.