Don't know about the "dead tired" part, but when I was busy with my hobbyist writing, my best story composition occurred between 10PM and 2AM. Other times, I would just clean up things, tweak my grammar and spelling (because fantasy fiction confuses spell checkers to no end...), and make notes related to later events needing resolution - the "loose ends" list.
Maybe it was because when dealing with magical creatures, daytime is a bad time to write about them? They only come out at night?