X-rays from high-mass X-ray binaries (HMXBs) are likely the main source of heating of the intergalactic medium (IGM) during Cosmic Dawn (CD), before the completion of reionization. This Epoch of Heating (EoH; z ∼10–15) should soon be detected via the redshifted 21-cm line from neutral hydrogen, allowing us to indirectly study the properties of HMXBs in the unseen, first galaxies. Low-redshift observations, as well as theoretical models, imply that the integrated X-ray luminosity to star formation rate of HMXBs (LX/SFR) should increase in metal-poor environments, typical of early galaxies. Here, we study the impact of the metallicity (Z) dependence of LX/SFR during the EoH. For our fiducial models, galaxies with star formation rates of order 10−3–$10^{-1}\, M_\odot$ yr−1 and metallicities of order 10−3–$10^{-2}\, Z_\odot$ are the dominant contributors to the X-ray background (XRB) during this period. Different LX/SFR–Z relations result in factors of ∼ 3 differences in these ranges, as well as in the mean IGM temperature and the large-scale 21-cm power, at a given redshift. We compute mock 21-cm observations adopting as a baseline a 1000 h integration with the upcoming Square Kilometer Array (SKA) for two different LX/SFR–Z relations. We perform inference on these mock observations using the common simplification of a constant LX/SFR, finding that constant LX/SFR models can recover the IGM evolution of the more complicated LX/SFR–Z simulations only during the EoH. At z < 10, where the typical galaxies are more polluted, constant LX/SFR models overpredict the XRB and its relative contribution to the early stages of the reionization.