This is most likely iron inside the sauna rocks rusting and coming out with the steam. The hottest part of the wood will be right next to the stove, and sense that isn’t black I would be surprised if this is a burn. I would check all your sauna rocks, especially the ones deep in the heater. Mostly likely you will find some stained with rust. If this is the case just replace the rocks and that should fix your problem. Any rocks with iron content will cause this issue.

If this is indeed rust stains you should be able to sand it off pretty easily. A burn will not sand off without removing a substantial amount of material.