You live in a house in North America with a 75-gallon power-vented gas-fired hot water heater.
The house has no chimney, which is why the power-vent feature is useful.
The instruction manual (PDF) states that the water heater works like this:
- When the water in the heater's tank isn't hot enough, the water heater starts up. It lights the burner and starts a fan motor.
- The burner heats the water, but it produces some exhaust gas.
- The power-venting blower fan forces the exhaust gas out through the side of the house.
- Once the water is hot enough, the burner and the fan motor shut down.
The water heater does have an electronic ignition system, but R' Mordechai Frankel writes that this is no problem.
You're worried about the blower fan motor. If you use enough hot water on Yom Tov, the fan motor will eventually start up along with the rest of the water heater. I know that it's fine to enlarge a fire during Yom Tov; but is it also okay to (indirectly) make an electric fan motor start and stop?