no you have a faulty diverter valve, you can get a repair kit and also a service kit, repair kit would probably do for yours, very easy repair or you could change the complete valve but a more difficult job to change,neither pipe should get hot while the HW only is running, you could try as already advised, remove the actuator no need to drain anything, its just a clip, and try moving the pin back and forth with some long nosed pliers , for all the time it takes you have nothing to lose