The first step is to remove dust from the inside of the radiator. A very simple trick is to point a hair dryer in the slots of the radiator, to make all the residue fall on the cloth or on the paper grounding.
If you do not have a hair dryer, you can also use a vacuum cleaner. Use a cartridge thin enough to fit into the slots of the radiator.
If you want to avoid using the two appliances, you can create a utensil to reach the most complicated areas. Use a long stick and attach a microfiber cloth to one end using adhesive tape.
Once the dust is removed from the radiator, it attaches to the tip of the stick a cloth soaked in water, vinegar and bicarbonate to remove dirt and other residues.