Your body falls asleep because your core temperature drops, not because you are tired. A sauna or a hot bath, roughly ninety minutes before bed, first drives that temperature up; afterwards it falls further and faster than it would on its own. That is why a sleep spa has a sauna and not a bar.
Falling asleep begins with a drop in your core temperature. To achieve it, your body moves heat to the skin of your hands and feet, where it sheds it — which is why warm feet and a cool room work so well together.
A sauna or a hot bath strengthens that process. The heat opens the blood vessels in your skin, and as soon as you step out, your body gives off heat through those open vessels faster than normal. Your core temperature therefore drops deeper than it would without that warming.
The effect isn't in the heat itself but in the fall afterwards. That is why timing matters more than duration: about ninety minutes beforehand, so the drop coincides with the moment you want to fall asleep.
You don't need a sauna. A hot bath or a hot shower of fifteen minutes, ninety minutes before bedtime, does essentially the same thing. What you do need is a cool bedroom — the drop has to have somewhere to go.
Two things undo the effect: alcohol, which disrupts temperature regulation and makes the second half of the night restless, and a brightly lit bathroom just before sleep.
A bed can only do good work if the rest is right. Anyone lying down in a warm room, with light on their retina and a glass of wine in them, notices little of any bed at all — and is in effect judging their evening, not their mattress.
That is exactly why a SleepSpa stay doesn't begin with the bed but with the sauna and the pool. Not as an extra, but because an honest trial demands that every other factor is in order.
About ninety minutes beforehand. The drop in your core temperature then coincides with the moment you want to fall asleep. Directly before getting into bed works less well, because you then get in still warmed up.
Cold works differently: in the short term it makes you more alert. In combination it can be useful — hot to warm up, briefly cold to come out by, and then take your time. It is the fall afterwards that you want.