The time it takes to start getting warm is due to the distance and flow rate, how much cold water has to be displaced. Plus a bit to warm up the pipes but cooper has a much lower heat capacity than water (1/10) so that is not very great.
How hot it will get eventually will depend on how much heat is lost by the pipes acting like radiators, a combination of the length (surface area) of pipe and how well it’s insulated.
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