To be realistic, those engine block heaters have been invented to even have chance to start an engine after an arctic cold night like -20 or -30 degrees C.
During our winters, it's not necessary. If the car is stored in a comfty garage with 0-10 degrees C it won't save tons of fuel either.
That's true, but I would have fitted one for convenience and comfort, more than anything.
On our old Ford Galaxy, I would have certainly appreciated the faster cabin heating and demisting. On cold winter days, you would only start to get warm air after several miles, and the interior of the car would still be cold. All the diesel versions of the car actually had a Webasto coolant heater fitted as standard, as the engine didn't produce enough heat to get itself up to operating temperature in cold weather.
Fuel economy was down from 30mpg to 20mpg when doing these runs exclusively, I was seriously considering fitting one when petrol was approaching £1.40 a litre in the UK. In 30-odd years of driving, I've never once put a car in a garage.
However, the Jazz HEV is a very different vehicle, and it may not make any appreciable difference to the fuel economy. As for warming the battery, I would have thought a pre-heater would help with that as soon as the system started up.