I recently installed a new shower head in the master bath because we moved the old shower head into the guest bathroom because the shower head in there wasn’t quite up to par on actually spraying water in an optimally usable fashion into the showering area. Part of the new showerhead is an overhead option and a hand-held showerhead on a hose. There is a switch that can be turned to switch the water back and forth between the two. From personal experience of both Rhiannon and myself, the water in the hose doesn’t move until the switch is set to use the hand held.
The water in the hose cools off over time.
Just because the water coming out of the overhead nozzle is warm doesn’t mean the water in the hose is warm.
However, it is an effective way to wake yourself up in the morning (my situation), or get a good laugh when the person in the shower screams like a little girl (me laughing at Rhiannon). (And she really does scream like a little girl, only louder.)