Depends on the brine. Usually I simmer...to help release the other spice/herb flavors I have in it. Then yes, it should be cooled before meat hits it. You want to try to keep it at 40° or below. If it goes much above toss in some ice cubes... not too may of course, then you'd be messing with the salt/cure concentrations.
If it's just a salt/cure brine, no need to simmer as long as you have all the solids dissolved. I start with a bit hig concentration and warm water, and chill with ice.