a guess: I suppose it depends on the efficiency of your hot water heater. If you had an 'instant on/hot' type system it might be beneficial to start with warmer water. Otherwise, I think you would use more fuel as you are warming an entire water heater full of water (again) and using more water waiting for that water to get to you.

Considering how the water supply is already messed up in places like here in Southern California...you want to conserve as much as you can.