Since I brew outside I always add the water to the mashtun (coleman xtreme cooler) first to get it up to temp, then add grain, check temps and top off with whatever temp water is needed to get to mash temp. I usually never have to touch it after that until sparge/mash-out.
The first time I used the cooler I added the grain first then the water and had to keep adding hot water to get it to temp. The temp also cooled faster and required adjustment the whole time.