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 ≈ 200-450 Mpc that have high specific star-formation rates of 3-9 Gyr −1 and metallicities near Z ≈ 0.3Z , 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 HMXB 0.5−8keV /SFR = 40.19 ± 0.06 and log L gas 0.5−2keV /SFR = 39.58 +0.17 −0.28 ; significantly elevated compared to local relations. The HMXB scaling is also somewhat higher than L HMXB 0.5−8keV -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 gas 0.5−2keV -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.