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In the UK your dishwasher is typically connected only to the cold water intake, so that’s not a problem unless you have multiple showers in your house… that said, water heaters are often limited to either heating or hot water (not both at the same time), but that’s not an issue in practice since you’re not going to be using the hot water for long periods of time.
Are you sure you don’t have some other software updating Firefox in the background?
Normally this only happens on Linux when your package manager updates Firefox while it’s running, and on Windows that doesn’t happen because Firefox updates itself only when you (re)start it.