Cold water is an option but takes longer to thaw. And hot water can easily spoil the meat. So your best bet is to start off with warm/room temperature water, and increase the temp of the water slightly when you need to heat it up.

I would recommend placing the rat in room temperature water for about an hour- hour and 1/2, and replacing the water every 30 minutes. Then when your rat is squishy and the head doesn’t feel cold, place it in warm water(about 85-95) for about 5-15 minutes. That should make the rat warm enough so that your snake can detect it.