Again, I think the quickest and most effective way to thaw a mouse is to put it in a ziploc bag and fill up your bathroom sink with hot water, then put the bag in the water for about 5minutes. Make sure you have something holding the bag down in the water though or it will float ^_^ When you thaw your mouse, try doing this next time. Don't be afraid to touch the mouse to see if its warm enough either. I got over that on my second mouse ^_^ If its warm to the touch, its probably warm enough, and if your BP still won't take it, put it back in the bag and try putting it directly under the faucet for a few seconds.
And if killing your rats makes ya feel bad, just pretend its one of those "Ebola" rats ^_^ If I have to do it for my BP when I get her, which I probably won't have to do since the one I want is already on F/T, I'll picture it infecting thousands of people with Ebola and I'm just doing my duty by eradicating it!