The current models of early star and galaxy formation are based upon the hierarchical growth of dark matter halos, within which the baryons condense into stars after cooling down from a hot diffuse phase. The latter is replenished by infall of outer gas into the halo potential wells; this includes a fraction previously expelled and preheated, due to momentum and energy fed back by the SNe which follow the star formation. We identify such an implied hot phase with the medium known to radiate powerful X-rays in clusters and in groups of galaxies. We show that the amount of the hot component required by the current star formation models is enough to be observable out to redshifts $z \approx 1.5$ in forthcoming deep surveys from {\it Chandra} and {\it XMM}, especially in case the star formation rate is high at such and earlier $z$. These X-ray emissions constitute a necessary counterpart, and will provide a much wanted probe of the SF process itself (in particular, of the SN feedback), to parallel and complement the currently debated data from optical and IR observations of the young stars.

13 pages, 2 figures, accepted for publicatin in ApJL