Q. Why is it cheaper to heat a house with an air conditioner than with an oil radiator?

A. An air conditioner is a heat pump ("pompe à chaleur"), it makes the cold air outside even colder, and the difference comes to the room as 'free' heat.
I would say, for a given floor space buy and install an AC that is rated for double that space.
If your living room is 25 sq.m it would be a good idea to use an AC rated for 50 sq.m.
Not only that will keep you warmer, but I also suspect a device running its full capacity is less power-efficient than a bigger device running half or 2/3 its capacity. But every room needs a separate blower (although several blowers may be connected to a single large outside compressor unit).
Finally, for better comfort the air movement needs to be minimized, and the blower should (again) be powerful enough (and large enough) to provide heating at low air speed.

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