[Piwoslaw]

The fan doesn't blow air over the fins, but out of slits on one side of the "control end". I wondered where the heat came from and thought that one of the fins was enclosed inside, but then realised that an extra heating element is simpler.

I'm not sure whether fan heaters are less efficient than oil radiators - both use electric resistive heat, so neither is very efficient. A fan heater's heat is (almost) instant on and off, while an oil radiator takes longer to warm up, but also longer to cool down. The fact that it radiates a larger part of its heat may make it more comfortable than a fan heater, so a slightly lower wattage can be used.

Putting a small fan to blow over the fins of the radiator you have will improve the distribution of the heat, but I doubt it'll improve efficiency.