Mitochondrial fatty acid beta-oxidation enzyme that catalyzes the third step of the beta-oxidation cycle for medium and short-chain 3-hydroxy fatty acyl-CoAs (C4 to C10) (PubMed:10231530, PubMed:11489939, PubMed:16725361). Plays a role in the control of insulin secretion by inhibiting the activation of glutamate dehydrogenase 1 (GLUD1), an enzyme that has an important role in regulating amino acid-induced insulin secretion (By similarity). Plays a role in the maintenance of normal spermatogenesis through the reduction of fatty acid accumulation in the testes (By similarity). {ECO:0000250|UniProtKB:Q61425, ECO:0000269|PubMed:10231530, ECO:0000269|PubMed:11489939, ECO:0000269|PubMed:16725361}. This is the function of ENSG00000138796 (HADH, hydroxyacyl-CoA dehydrogenase).