The splay and bend elastic constants of the bent-core oxadiazole material [C5-Ph-ODBP-Ph-OC12] have been investigated as a function of temperature across the nematic phase. The bend constant K-33 is found to take values of similar to 3.0 pN and to be almost temperature independent, whereas, the splay constant K-11 increases monotonically from similar to 3.5 pN close to the isotropic phase transition to values of similar to 9 pN deep in the nematic phase. No pretransitional divergence is observed in either K-11 or K-33 at temperatures approaching the underlying phase. This behavior of the elastic constants is distinct from that observed in rodlike liquid crystal systems but appears to share characteristics with the few other bent-core nematic systems studied to date. We discuss the interdependence of the elastic constants, the birefringence, and the order parameter to allow a comparison of the observed behavior with theory. We show that calculations of the elastic constants via molecular-field theory and atomistic modeling are in excellent qualitative as well as good quantitative (within 2 pN) agreement with the measurements across the temperature range, offering a deeper understanding of the elasticity in bent-core nematic materials than has been, hitherto, available.