How do I add a custom thumbnail to a .mp4 file using ffmpeg?

As in version 4.2.2...See Section 5.4 in FFmpeg documentation

To add an embedded cover/thumbnail:

ffmpeg -i in.mp4 -i IMAGE -map 0 -map 1 -c copy -c:v:1 png -disposition:v:1 attached_pic out.mp4

Not all muxers support embedded thumbnails, and those who do, only support a few formats, like JPEG or PNG.

Using ffmpeg 4.0, released Apr 20 2018 or newer,

ffmpeg -i video.mp4 -i image.png -map 1 -map 0 -c copy -disposition:0 attached_pic out.mp4