Heating when the power is off.

[Mortblanc]

A small battery powered fan might help disperse that warm air into the living space.

You did not say how many gallons of hot water you have on hand in the system.

Over here we still use "water heaters" that contain the hot water and keep it heated by thermostat. My own is a 120L tank and I keep it heated at 50c. I know from experience that it remains hot enough for a good hot shower for 24 hours after being separated from its electric power source.