On 7/9/2015 10:36 PM, HerHusband wrote:
Tankless heaters are generally rated for a given temperature rise at
a given flow rate. If you draw water faster than it can heat it,
you'll get cooler water.

This isn't his problem. The problem is that tankless heater is not
heating to a specific temperature regardless of the flow rate so at
low flow the water is too hot.

If the water is too hot at low flow, there are two likely causes:

1. The water heater is set at too high of a temperature.

2. The pressure balance valve in the shower faucet is defective.

Both are easy fixes.

Does any tankless hot water heater monitor the flow rate and output
temperature and then adjust the flame to keep the temperature constant
regardless of the flow?

I have no idea, but a standard tank model doesn't do this either.

Wrong.

The temperature of the water out of tank model is constant regardless of
the flow rate. Sure you can drain it faster than it can re-heat the
water if the flow rate is very high, but that is not the normal case in
a properly sized tank heater.

A tankless model could mix cold water with hot water at lower flow rates
to keep the output temperature constant (rather than trying to adjust
the flame intensity. Maybe some do this.