AGREED,when I suggested the t stat before I was thinking of,"somewhere", I read about an engine that either had a small hole in the t stat or a bypass around it so some cool water would always flow thru when it was closed,preventing 'cold shock" when it opened.
Now, I cannot find where I read it!!. Thought it was in the h3 book but not so.
I'm thinking the t stat sticks till its real hot , then pops open wjth more flow with higher engine speed. Regardless, the obvious move is to change it.

later. I found discussions about this. It can happen if there is an air block stopping a complete refill. Some engines have a hole in the t stat. A few guys say they nearly ruined engines that had no vent for complete refill,"hot heads'!
Lots of info out there.