Would you paint aluminum radiator?

If you do paint, do so right away. Paint doesn't bond well to oxidized aluminum. Indeed, even bare aluminum already has slight surface oxidation so many paints don't stick (read can). The thin paint layer shouldn't change the heat transfer much and might even exceed that of oxidized aluminum you will get without paint. The white powder is aluminum oxide, in crystalline form known as "sapphire". All the metal in your car is striving to return to the earth.