There is no gay sauna in Punta Arenas or anywhere in Magallanes. The "gay saunas" that turn up online are couples' motels (Motel Eros, Las Mil y Una Noches), a massage centre and the spa of the Dreams hotel.
The nearest gay saunas we list are in Santiago, more than 2,000 km north. For everything else in the city, see our Punta Arenas guide.