well yeah COLD is a discomfort. Discomfort keeps one from sleep. But just a little cold could deliver only slight Discomfort. Taking a Warm shower makes you really drowsy, relaxed and sleepy. Taking a Cold shower makes you very alert and awake.

So maybe we could try taking different temperature showers right before sleep might do this trick as well.

And if Warmth works better for you to have lighter sleep. well then just use this technique in the opposite way. People differ.