Block heaters can be used to heat the engine coolant (and afterwards the cabin) with or without running the engine. I doubt any cars have special batteries for

Block heaters can be used to heat the engine coolant (and afterwards the cabin) with or without running the engine. I doubt any cars have special batteries for these (even a drive battery of a non-plugin hybrid is somewhat small to be useful); block heaters that don't require external electricity simply use the car's fuel in an auxiliary burner.