  While there is now a consensus that X-ray binaries (XRBs) are the dominant
X-ray sources in the early Universe and play a significant role during the
epoch of heating of the intergalactic medium (IGM), recent studies report
contradicting results regarding their contribution in the nebular emission of
local Universe galaxies. Ultraluminous X-ray sources (ULXs), which dominate the
X-ray budget of normal galaxies, may be important interstellar-medium (ISM)
ionizing sources. However, their output in the extreme UV (EUV) and soft--X-ray
part of the spectrum remains observationally unconstrained. In this paper, we
predict the ionizing and heating power from ULX populations under the
geometrical beaming scenario, and three models describing the emission from
super-critical accretion disks. We find that our theoretical spectra for ULX
populations cannot (can) explain the HeII (NeV) emission observed in some
galaxies, with their contribution being less (more) important than the
underlying stellar population. Stochastic fluctuations in the number of ULXs
may allow for equal contributions in the HeII emission, in a fraction of
galaxies. We provide average spectra of ULX populations as an input to local,
and early-Universe studies. We find that the soft--X-ray emission arising from
super-critical accretion is significant for the heating of the IGM, and
consistent with recent constraints from the 21-cm cosmic signal. Based on the
dependence on the adopted compact-object (CO) mass and accretion model, we
encourage efforts in modeling ULX spectra via simulations, and their
combination with detailed binary population synthesis models.
