A major problem for F1 designers is cooling the various components - mainly the engine and transmission. If the radiators are made too large they will be heavy and the air directed through them will generate excessive drag. So the radiators are made as small and light as possible and designed to be effective when the car is moving at racing speeds. As F1 cars do not have radiator fans the coolant temperature rises rapidly when the cars are stationary on the starting grid, which is why the starting procedure attempts to minimise this time.
Similar concerns relate to the brakes - ducts direct cooling air onto the brake callipers and discs, but these must be made as small as possible to minimise drag.