[Thrymr]

A gas boiler furnace with steam radiators typically only requires power for the thermostat and solenoid valve, which can indeed be powered by a small battery. This is assuming you have a pilot light, which many older furnaces do.

[JshWright]

Residential steam boilers are pretty rare these days. Generally hot water heat uses circulation pumps (which draw less than a forced air blower, but still have a non-trivial continuous current draw)