Hello: The easy way to tell if it’s the mixing valve is to have someone run hot water while you feel the valve and associated piping. If cold water is being fed into it and the hot outlet cools down to below the set point of the valve, you’ll know the mixer is misbehaving. Thing is, I’d expect it to happen right away, not after twelve minutes.
Another possibility is cold water flowing backwards through the recirc system. Checking that also to see if it goes cold after some use will be instructive 😎