The method works, and I am going to elaborate on it a little. As the poster said, start warm, work your way down to cool, then cold. Very cold.
But what really seems to kick one off to dreamland is not drying your hair, instead putting a towel down on your pillow. As your hair dries, you'll get some more evaporative cooling strictly for your head, and that helps even more
Have you tried a hot shower instead just before the bed. The trick is that it cools down the core when you leave bathroom (by bringing blood to the surface).
Extremities should be warm, the core(CBT)—cold, to fall asleep easier.