It turned out that the Levi Hotel Spa had been extended greatly in the meantime. It was a truly great place now, with outdoor pool, 2 outdoor hot jacuzzis, two new saunas -- steam and kelo -- and plenty of new pools and even a waterslide inside. Much recommended!
The visit to the spa is free for hotel guests, but if you're not a guest -- like me, sleeping in my car on this trip :-) -- it costs 22€ per visit. But there was a Plussakortti-tarjous for 15€, which was quite reasonable for this kind of a spa.