Until a couple years ago we had a gas-fired tankless water heater which used a single D-cell battery for ignition, which had to be changed once every year or two. It wasn't connected to wall power at all.
There are, or used to be, Bosch tankless water heaters which used a small turbine connected to a piezo-electric igniter, no external power source required ever.
But you need a blower or pump in order to circulate heat in a house. Hot water is better than nothing but it won't keep your fish from freezing.
I have a sol-ark 12k which allows for grid isolation and a bunch of batteries.