Treat it like any other component overheating problem. Is there good airflow over the drive, or is it nuzzled at the bottom of your case between two hard drives and a rats nest of cables? Is it mounted on the motherboard back plate?

More info will let us help you more. What’s the temperature of the drive during these large file transfers? What’s the max temp before it powers off and is no longer detected?

That’s just the year of the movie. Files don’t actually need extensions (like .mp4 or .mkv) to work a lot of the time. VLC reads the first x bytes of the file and recognizes it as a video file, then plays it anyway.