One of the exciting frontiers in astronomy is the era of the formation of the first stars. Since the Universe was filled with hydrogen atoms at that time, the most promising method for observing this epoch is via the prominent 21-cm line of hydrogen. Several international groups have begun operating new arrays of radio telescopes, hoping to open this new observational window on the early Universe. The common view has been that they can only search for cosmic reionization (in which radiation from stars broke up the intergalactic hydrogen atoms), while other cosmic events occurred too early to see. However, we recently overturned this long-held view, arguing for a late and uniform heating given the hard spectrum expected for the sources of X-ray heating (most likely some of the first black-hole binaries). Cosmic heating therefore imprints a clear, previously unexpected signature in radio waves, perhaps within reach of current arrays.