Pre-war aircraft commonly had a fabric exterior. Metal (aluminium) aircraft came along in the late 1930s, some painted, some not. "Aluminium" is typically an alloy with various other minority metals (chromium, copper, etc), some alloys are more suited to not being painted that others. Different designers would specify different alloys, and the ability of the aluminium producers in different parts of the world to offer different products also came into it. Different air forces also had different attitudes to camouflage and visibility. Eventually a non-painted exterior, outside camouflage requirements, prevailed of course.
In the late 1940s BOAC had a significant issue with (unpainted aluminium aircraft) flight decks becoming too hot when cruising in the tropics under overhead sun, with the poor air conditioning of the time. Whoever first thought of painting above the flight deck white to reflect the sun, quickly followed by the rest of the upper fuselage, set the style for the rest of the airline industry to follow. Apart from American Airlines, who never painted an aircraft from their first aluminium one in the 1930s until about 5 years ago, when they finally gave in. It saved weight, but was offset quite a bit by extra maintenance resulting.