Apple TV 3rd generation. How to download to device
The Apple TV 3rd Gen has no true storage at all &amp; only 512MB RAM - it was discovered it does actually have a 'hidden' 8GB, but presumably that will be caching content for immediate use rather than storing a movie you watched previously.
38 minutes to download a movie/TV show would indicate your internet connection is struggling.
From Everymac -

*Officially, the third generation Apple TV models have no internal storage. However, third-parties have determined that they actually have 8 GB of flash memory to cache content, just like the second generation Apple TV.