Tankless point of use water heater that only heats when inlet is cold
TLDR: they all do that, it's a safety feature to avoid scalding. 

It takes a lot of power to make heat.  

You won't get much heat out of a 120V on-demand heater unless you really, really, really restrict water flow, like, you could get a cup of tea out of it if you're patient.    Don't even bother with on-demand unless you are willing to run 240V to the heater and at least 20A preferably 30.  

An on-demand heater made to run alone on a 15A circuit, is 1440W.  It will only embarrass itself and its entire class of heaters.  You will be disappointed, swear them off for good, and that will be a shame because they are wonderful when you size them properly. 

As others discuss, they have safety controls to prevent outputting scalding water.  You should not set your on-demand heater to scalding to avoid legionella, legionella can't grow in an on-demand.   You should set your tank heater to kill legionella.