Radiant heat doesn't heat air. Conductive heat transfers by heating air. Radiant heat doesn't transfer by heating air. It is the transfers through air of radiant energy from a warm object to cooler objects. Therefore the warmer mass will give the cooler mass its heat.
Air is heated incidentally by a radiant heating system.
A Delta W arm system will transfer heat from your entire floor surface to cooler objects in the room. The air in which the heat is traveling will be heated incidentally. The Sun A primary source of radiant heat for the entire planet is the sun. That's why a breeze feels cool on a hot day.