I agree with everything the other posters said. I place my mice/rats in a zip lock bag and then put that in cool water to thaw. After about 20 minutes I will empty the water and refill with warm water for 10 minutes. When that is done I take it out and I blow-dry the mouse to warm it up.
Now one thing I do differently is that I blow dry the mouse right next to the cage. My two BP's will smell the upcoming meal and come looking for it (it's one way I know they are hungry). I also have a small temperature gun and quickly check the prey's temperature and make sure it is in the mid to upper 80's. You can do this check by hand and holding the mouse but I'm trying to teach my kids how to feed the animals and my wife doesn't want them touching dead mice. Once the food is ready I open the cage, dangle it a little with tongs, and they do their thing.