The low temperatures allow the gas to contract gravitationally to form stars, so without radio and infrared astronomy, there would be no way to observe how stars are born. As a body's temperature increases, it can radiate at higher energies. At a few hundred degrees above absolute zero, objects radiate strongly in the shorter wave infrared. That's why an infrared camera can take your picture at night. Astronomers use infrared light to study the advanced stages of star formation and warm dust ejected by dying stars.
Cool stars radiate most of their energy in the infrared.
Hot stars radiate mostly in the ultraviolet, so without examination of these spectral bands, astronomers would lack a great deal of important information. What begins as a single gamma ray photon in the sun's core emerges at the surface as thousands of visible-light photons. Our sun appears relatively quiescent when viewed in visible light. But an examination in x rays reveals spectacular loops of gas heated to millions of degrees by solar magnetism. Without this knowledge, astronomers can make no sense of the solar wind, solar activity, and their effects on Earth.