Guest
It probably has everything to do with pressure, or more precisely pressure differentials between the hot and cold pipes. I assume this is a tankless water heater, so the velocity of the water through it will affeect the output temperature, although 13kw should be adequate for most showers as long as no other hot water is being used at the same time. Your money might have been wiser spent on a pressure balanced shower valve which would compensate for the pressure changes.
