Not knowing anything about your plumbing we can only relate your problem to the systems we have on our own boats. In our case, the fresh water pump applies pressure via an accumulator tank to the water coming from the water tanks. The pump runs as it pressurizes the accumulator tank and then shuts off until the pressure in the tank has dropped to a certain point and then the pump kicks back in. The cycle rate varies with the water demand. With a low demand, say a sink tap on at a fairly low flow, the pump is on for about 2 seconds and then off for about 2 seconds. Or maybe a bit faster. But under high demand, like a shower, the pump simply stays on. The accumulator tank is there to keep the water flow to the system at a fairly constant pressure instead of pulsing as the pump cycles.
On our boat the pressurized water is fed to the cold water taps and to the hot water heater. So turning on a hot water tap reduces the pressure in the whole system which starts the pump going which pressurizes the system and forces hot water out of the hot water tank and through the hot water hoses to the sink taps and shower. So on our boat, at any rate, I cannot think of any way the pump could cause a cycling between hot and cold water in the shower head. It's simply pressurizing the whole system.
Now I suppose it's possible for a partial hose blockage or something to prevent the full pressure from reaching the hot water tank, so when the pump cycles off when the accumulator tank (assuming you have one) is up to pressure, I suppose it might be possible for the lesser resistance in the cold side of the system to over-ride the reduced pressure on the hot side until the pump kicks back in again. But I'm speculating here and this theory could be total BS.
Perhaps if you could describe the actual pump and plumbing layout in your boat someone on this forum with more water system experience than me could suggest some causes of the problem you're experiencing.
-- Edited by Marin on Saturday 24th of October 2009 09:12:25 PM