The walls and ceiling in any Finnish sauna are always made of wood. While brick walls would make for a great "look", it does not make for a good sauna room. These walls should be framed, insulated, and built the same as the others for a comfortable and consistent sauna bathing environment.
Brick walls are common in another type of sweat bath, known as Temazcal. Call a Sauna Specialist
to explore the options for your installation.