I put my mice in a plastic sealed bag, put the hottest water that will come from the tap into the sink, weigh the bag down with coffee cups so it will stay submerged, and they're normally thawed within 20 minutes or so.
The way I can tell is when I pick them up, they're warm to the touch throughout the body and they're flexible and fleshy. I usually give them a small "squish" or a "roll" with my fingers when I think they're thawed out to make sure there are no cool spots anywhere on the body.