> Just the thought of looking at a watch in a sauna

You don't take your watch into the sauna! It's way too hot! I use a plain mechanical kitchen timer (outside the sauna). I've seen hourglasses that are designed to withstand the heat inside the sauna, but they're obviously not configurable to various increments.

More seriously: apparently studies show that using a Finnish (dry) sauna 5-7 times a week is good for longevity. You don't have to use them that way, but if that's your goal, it probably makes sense to fit it into your routine, and it's tough to do that without planning how long it will take.