I have a tankless water heater. It takes 3 seconds for it to detect a flow, and 3 seconds to heat up. So, assuming cold water in the (output) pipes, it takes however long it takes for all the existing water to run through the pipes (call this T1) PLUS 6 seconds for hot water to come out of the tap. ok so far.
What happens though is that after getting hot water and then shutting off the tap, there is now a 6 second cold water "void" in the pipes. so hot water comes out for T1 seconds, then 6 seconds of cold water, then hot again.
This is annoying if, e.g., you run the shower, then use hot water at the sink. Initially it's hot, but then it goes cold.
Any ideas on how to fix this? I'd thought of having a recirc pump and/or a small storage tank, but I'm not sure that either one will address the problem adequately if at all.