  Using a reliably measured intrinsic (i.e. corrected for absorption effects)
present-day luminosity function of high-mass X-ray binaries (HMXBs) in the
0.25-2 keV energy band per unit star-formation rate, we estimate the preheating
of the early Universe by soft X-rays from such systems. We find that X-ray
irradiation, mainly executed by ultraluminous and supersoft ultraluminous X-ray
sources with luminosity L> 10^39 erg/s, could significantly heat (T>T_cmb,
where T_cmb is the temperature of the cosmic microwave background) the
intergalactic medium by z~10 if the specific X-ray emissivity of the young
stellar population in the early Universe was an order of magnitude higher than
at the present epoch (which is possible due to the low metallicity of the first
galaxies) and the soft X-ray emission from HMXBs did not suffer strong
absorption within their galaxies. This makes it possible to observe the 21 cm
line of neutral hydrogen in emission from redshifts z<10.
