Cutter Is it possible for tvheadend to automatically take a screenshot
Automatically, not that I am aware of.
You could look into creating a script (Configuration -> Recording -> Digital Video Recorder Profiles -> Miscellaneous Settings -> Post-processor command) that runs after a recording is complete. That script could use something like ffmpeg
to extract thumbnail images.
Once you have the thumbnails, you would need to know now Kodi or other clients expect to find the thumbnails in order to present them.