Abstract: We report the results of the energy dependence of specific heat (C_V) of hadronic matter in a multiphase transport (AMPT) model and compared with the experimental results from Ref.PhysRevC.94.044901. The temperature high order fluctuations in Au+Au collisions in AMPT model are also reported. C_V is a thermodynamic quantity that characterizes the equation of state of the system. For a system undergoing phase transition, C_V is expected to diverge at the critical point. Fluctuations of temperature are sensitive observables to probe the QCD critical point. The C_V is extracted by analyzing the data on event-by-event mean transverse momentum (<p_T>). The <p_T> distributions in finite p_T ranges are converted to distributions of effective temperature (Teff). The C_V is extracted from the T_eff distributions. The fluctuations of temperature are measured by calculating the high order cumulants of the T_eff distributions. We find that both C_V and high order cumulants of the temperature show monotonic distributions in energy dependence, which is expected that there is no phase transition critical point in the AMPT model. At low energies, a sharp drop of C_V from the experimetal results is observed and it deviates from the AMPT results. The AMPT model can provide a non-critical background, which can provides a good reference for comparison with experimental results to search for the QCD critical point.