Yeah. I like to think that "Class-M" and "Minshara
-class" just happen to both start with the letter M.
I'm not sure that temperature is the main qualifier of what class of planet one is, but is one of numerous factors in the over all habitability of a given world. Things like Atmosphere composisiton, gravity, exposure to radiation and other features no doubt play a role as well. But I agree that the closer to "M" in the middle are the habitable worlds.