http://edition.cnn.com/2016/11/10/travel/helsinki-finnish-sauna-guide/index.html
I guess the reason why sauna prevailed in Finland is that finnish sauna is sophisticated and evolved to fit contemporary society.
But, the oldest culture that had sauna is in Mexico or Central America.
It's a good example that winner is not an inventor of something, but is the one who succeeded to make it common.