Electric cooling fan wiring question

So, I can just hook the yellow wire (trigger wire?) up directly to the battery and it will do what it needs to do? And if I turn the car off hot, the fans might run for a while until it drops below the preset temp? That might not be a bad way to go. Think I'll give that a shot, and if I don't like it, I'll find a key-on hot wire to tap into.

Thanks!