Frequency-dependence of specific heat in supercooled hard sphere liquid is computed using quantum mode-coupling theory (QMCT). Mode-coupling equations are solved using a recently proposed perturbative method that allows us to study relaxation in the moderate quantum regime where quantum effects assist liquid to glass transition. Zwanzig’s formulation is used to compute the frequency-dependent specific heat in the supercooled state using dynamical information from QMCT. Specific heat shows strong variation as the quantumness of the liquid is changed, which becomes more significant as density is increased. It is found that, near the transition point, different dynamical modes contribute to specific heat in classical and quantum liquids.