We report on the phonon spectrum of the spin-gapped quantum magnet Ba3Cr2O8 determined by infrared spectroscopy, and on specific heat measurements across the Jahn-Teller transition in magnetic fields up to 9 T. Phonon modes split below the Jahn-Teller transition, which occurs at TJT=70 K as detected by specific-heat measurements. The field-dependent specific heat data is analyzed in terms of the contributions from lattice, magnetic and orbital degrees of freedom. In contrast to the isostructural compound Sr3Cr2O8, our analysis does not indicate the existence of orbital fluctuations below the Jahn-Teller transition in Ba3Cr2O8.