At least you could quickly determine where all of the working circuits go, which may narrow it down some. Sometimes, a good visual inspection is all...
FWIW, the tempering valve only adds cold to the outlet of the WH IF it is above what's left in the tank...IOW, if say the WH was set to 140, it would...
The first time someone (it's usually the young or old who have the thinnest skin and get the worst of it) comes out with second degree burns because...
Where I live, regardless of how hot you set your WH tank to, you are required to install a tempering valve. Now, they come preset to 120-(maybe 119)...