Thawing frozen in a bag?

Instead of putting the bare rats and mice in the hot water can I thaw them while they are in the bag? I hate it when little aspen shavings get on them and into my snakes mouth. Its not hard to remove but when it happens all the time it gets annoying. Especially when I cant get it all.

So can I thaw them in a bag? And if so will the time thawing be around the same ? I usually just put the tap on and wait till it gets to the hottest it can and put them.

This is how I prepare F/T food

1. Get zip lock bag
2. Place food in it
3. let thaw in hot water
4. Remove from zip lock and let it sit under heat lamp for 10-15 mins after food is thawed
5. Give to your snake :D

One of my snakes is still kept on wood chips and I had that same problem. I fill the sink up with a little bit of room temp water and put the rat in a plastic baggy and let it soak til its soft. Once its thawed, I get the water real hot and let it sit for a couple mins so that the rat is nice and warm and then ur good to go.