If you are playing youtube video online, actually the video has been saved on local disk. The video saved in temporary file type. The video will be exist until the youtube video page closed.
1. Play your youtube video favorite until the end of video.
2. Check your mozilla chace location:
The temporary file will be saved on Mozilla Firefox cache. The extension should be .tmp
3. Copy address cache directory to explorer
4. Rename the temporary file to become .flv extension
5. Play the video using flv player