I'm basing your answer on this phrase in your poste:
"...then after some time when the stainless steel pipe is cold, get the drinking water in."
If you are interested in seeing how your system cools the fluid then you may want to set initial conditions for both fluid domains and both solid bodies for the cool temperature then start the analysis by sending the warm water through your pipe. This, of course, would assume that your system has cooled the pipe to a steady state temperature with no water flowing through the pipe. The fluid inlet for your pipe would then be at the warmer temperature and be cooled by the initial temperature of the system and the continual pumping of coolant through that tube as well.
You would also turn on the the time dependence of the flow project and periodic saving in order to see the change over time but it seems like a fairly straight forward setup to run.