They slow down without any heat, and tend to just sit still. Now they're still all wrapped around, over, and under each other, but as far as motion is concerned, it just doesn't happen. Now imagine trying to drive a bulldozer through this room full of snakes. If it is warm, and the snakes are moving, they can quickly slither out of your way, and the bulldozer moves through the room, causing a minimal amount of snake damage. But if its cold, one of two things will happen to the motionless snakes.
Polymers are the same way.
When the temperature is warm, the polymer chains can move around easily. So, when you take a piece of the polymer and bend it, the molecules, being in motion already, have no trouble moving into new positions to relieve the stress you have placed on them. But if you try to bend sample of a polymer below its T g, the polymer chains won't be able to move into new positions to relieve the stress which you have placed on them. So just like in the example of a room full of cold snakes, one of two things will happen. It is actually an effect of random motion of molecules, whether they are polymer molecules or small molecules.