Recently I will turn on the water, a mix of hot and cold to get temp right. Then the water will pulse between hot and cold. First experienced it in the shower, then the bath sink, and then the kitch...
Showers not being turned off with knobs...just the button on handle allow hot/cold to mix in the faucet Water heater 'Bypass' valve open/leaking thru allow hot/cold to mix
Water heater Hot out check valve clogging can cause hot water flow to fluctuate
Atwood XT Models with mixing valve...clogged mixing valve can cause hot/cold fluctuations
Water pump cycling on/off due to low demand/flow can cause it also