Radiators heat passively: they warm the nearby air, which rises and allows cooler air to flow in. This new air then warms, and the cycle repeats. This works pretty well: no electricity, no noise, just smooth heating.

What we can do with a fan, though, is accelerate this process in a targeted way, at the cost of a small amount of electricity, hardware, and noise. By fanning the radiator we want more output from, we can bring the system into balance.

I'm now tempted to put efficient little fans on all the radiators in the house, network them together, add temperature and occupancy sensors, predict future occupancy, and see how much more efficient I can make the whole system. But while this sounds like a fun project, and possibly even something someone could turn into a product that pays for itself in saved money and fuel, [1] this is really not something I should take on right now.

[1] I did some looking and there are (a) commercial radiator booster fans, and (b) smart radiator valves, but nothing that ties this all together.