Japan has a +4 years lead of life expectancy over Finland; Norway almost +3 years on Finland. I am not saying this is conclusive per se, but to me the sauna-people-live-forever is not backed up by the data. I would instead reason that, e. g. weight correlates a lot more here.
Nobody is claiming they live forever. The claim is sauna use increases lifespan. There are other factors than just sauna use in lifespan though. The question is would the Japanese live even longer if they were using a sauna?
A lot of Mediterranean countries also have high life expectancy and are the opposite of a sauna culture.
Cyprus summers are like 45C and its almost like a sauna :)
Maybe eating a lot of fish, rather than meat, has an impact too.