Models and simulations of the epoch of reionization predict that spectra of the 21-cm transition of atomic hydrogen will show a clear fluctuation peak, at a redshift and scale, respectively, that mark the central stage of reionization and the characteristic size of ionized bubbles. This is based on the assumption that the cosmic gas was heated by stellar remnants - particularly X-ray binaries - to temperatures well above the cosmic microwave background at that time (~ 30 K). Here we show instead that the hard spectra (that is, spectra with more high-energy photons than low-energy photons) of X-ray binaries make such heating ineffective, resulting in a delayed and spatially uniform heating that modifies the 21-cm signature of reionization. Rather than looking for a simple rise and fall of the large-scale fluctuations (peaking at several millikelvin), we must expect a more complex signal also featuring a distinct minimum (at less than a millikelvin) that marks the rise of the cosmic mean gas temperature above the microwave background. Observing this signal, possibly with radio telescopes in operation today, will demonstrate the presence of a cosmic background of hard X-rays at that early time.
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