  High-energy emission associated with star formation has been proposed as a
significant source of interstellar medium (ISM) ionization in low-metallicity
starbursts and an important contributor to the heating of the intergalactic
medium (IGM) in the high-redshift ($z > 8$) Universe. Using Chandra
observations of a sample of 30 galaxies at $D \approx$~200--450 Mpc that have
high specific star-formation rates of 3--9 Gyr$^{-1}$ and metallicities near $Z
\approx 0.3 Z_\odot$, we provide new measurements of the average 0.5--8 keV
spectral shape and normalization per unit star-formation rate (SFR). We model
the sample-combined X-ray spectrum as a combination of hot gas and high-mass
X-ray binary (HMXB) populations and constrain their relative contributions. We
derive scaling relations of $\log L_{\rm 0.5-8 keV}^{\rm HMXB}$/SFR $= 40.19
\pm 0.06$ and $\log L_{\rm 0.5-2 keV}^{\rm gas}$/SFR $= 39.58^{+0.17}_{-0.28}$;
significantly elevated compared to local relations. The HMXB scaling is also
somewhat higher than $L_{\rm 0.5-8 keV}^{\rm HMXB}$-SFR-$Z$ relations presented
in the literature, potentially due to our galaxies having relatively low HMXB
obscuration and young and X-ray luminous stellar populations. The elevation of
the hot gas scaling relation is at the level expected for diminished
attenuation due to a reduction of metals; however, we cannot conclude that an
$L_{\rm 0.5-2 keV}^{\rm gas}$-SFR-$Z$ relation is driven solely by changes in
ISM metal content. Finally, we present SFR-scaled spectral models (both
emergent and intrinsic) that span the X-ray--to--IR band, providing new
benchmarks for studies of the impact of ISM ionization and IGM heating in the
early Universe.
