Specific thoughts on baby in sauna with temperatures

I read the "children in the sauna" post and saw some good guidance, but also wanted to check in with a specific age and temps in mind. My son just turned one and is quite hardy. (The sauna we're planning to visit is Washington Baths in Portland, ME if anyone has been and has thoughts on the logistics/how interruptive to everyone else it might be based on the vibe there...) The owners said he is welcome to come in. I asked about temperatures, and they replied: "The temp of the hot pool is in the range of 104-105F, temp of the cold pool is usually around 48F, and the temp of the sauna varies quite a bit depending how high up you sit: at the top it is in the range of 180-200F, at the bottom probably closer to 100-120F."

We have a small, foldable Stokke brand baby tub, and based on the advice in this sub, I was considering bringing that along in (also going at an off-time on Monday so hopefully not in the way of too many people) and letting him play in that on the floor. However, if he's only going to be able to do one or two minutes at a time, is that something worth inconveniencing others over in your opinion?

I'm not thinking of taking him into the cold tub and probably not the hot tub, though depending on circumstance I can see myself holding him in there for a short period.

Thoughts?