Was the problem after the water was already hot at the tap then it was thermal overload, the heater will overheat the water go off on high limit and then wait for the water to cool to restart again, but in the waiting period cold water will flow thru the heat exchanger into the tap. The rinnai should have been set to work at 50% of the load, it will take the same amount of time to heat but it will run on low fire at first then go to high fire if needed....if it was when you first open the tap that's normal since stopped water will cool, a recirculating pump bringing the hot water back to the heater would have that problem.
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