I'm really kind of on the bench regarding cold showers and sleep inducing. I feel that the "shock" of a cold shower, coupled with the narrowing of the capillaries and keeping the warm blood in the core might act contrary to what Robb suggested, at least in some cases. I have used cold showers between lifts at PL competitions, and between matches during my high school wrestling career to get "up" for the coming event.
I am not sure a cold shower is of the duration to cool down the core of the body.
Now, hot showers, on the other hand, have that vasodilation effect, with the body seeking to shed the additional heat, and, that, in turn will allow the core to cool faster.
It's an interesting subject. I don't know what point of view is the most valid, or if it's conditional.