You could try trapping her by baiting the rat in her enclosure with the heat pack working under the cage. If she goes and eats, she will most likely hide (hopefully you have a good hide, not a log hide) in a dark spot and digest.
Just putting the cage on the floor is fine.
Snakes rarely ever leave the room if they escape. They have little energy to waste, and probably just wanted to find a warmer, darker place to hide. Usually they will be within 6ft of the enclosure when found.
Also, I doubt the snake would be able to get out of the room (closed doors in all) and not be noticed in the halls.