On some bad advice I had a new hot water heater installed and have the same problem.
2100sq.ft.house with 2 1/2 baths. Three people in the house. It takes 2 to 3 minutes
To get hot water at a faucet or any other outlet. Now I'm told that I need a thermal expansion tank between the main water line and the hot water heater. The cold water line to the hot water tank is very warm to the touch.