Hot water temperature fluctuating

A tankless unit holds temperature by modulating its burner against the flow it senses. Open a second fixture and the flow splits; if the combined demand exceeds what the unit can deliver at the current inlet temperature, the outlet temperature falls until the first fixture closes, then spikes back. That surging hot-cold-hot pattern is the signature of a unit at its flow limit, and in winter it appears at lower flows because the rise is larger.

The other tankless causes are mechanical: a fouled inlet filter or flow sensor makes the unit misread demand, and a scaled heat exchanger reduces output. If the pattern follows filter age or appeared after years of service, the descaling and filter service is the first step, with the flow-at-rise arithmetic checked at the same visit.

On a tank, temperature fluctuation at a shower is usually plumbing, not heating: a broken dip tube lets cold incoming water short-circuit straight up to the hot outlet, so the shower runs hot, then mixes cold, then recovers as the tank reheats. The same symptom can come from a crossed or failing mixing valve, or from two tanks or a recirculation loop mixing at the fixture.

A control that cannot hold temperature is the heater-side cause: a failing thermostat or gas control on a gas tank, or a failing element/thermostat pair on an electric tank. These are diagnosed by measuring outlet temperature over time rather than by replacing parts on the symptom.

The pattern is the diagnosis. Note when the swing happens (only with two fixtures open? only in winter? only after the tank has been idle?), how wide the swing is, and whether any fixture is affected or just one. A fluctuation at one shower with everything else steady points at that shower's mixing valve; a whole-house swing points at the heater or the distribution.