If you leave a "sated warmonger" to governing he will eventually lose the "sated warmonger" and become a "warmonger" again. If he doesn't get battles then, he might even become a "restless warmonger", which is a negative trait.
You should really try to specialize your FMs. Some battles don't hurt, but once you reach "warmonger" using him as a governor is a two edged sword.