We studied the energy dependence of specific heat extracted from the fluctuation of temperature fitted by the pT spectra at √ sNN = 7.7 GeV to 200 GeV in Au + Au collisions by using AMPT model. The results were compared with those from other models and some difference at low √ sNN was found. To explain the difference and describe the properties of the hot matter at low √ sNN , we derived new quantities C ξ v and C ξ * v for describing specific heat in heavy-ion collisions. We found that the alternative method could describe thermal properties of the matter involving C ξ * v together with its high order moments, namely skewness and kurtosis, extracted from the event-by-event distribution of C ξ * v . The proposed observables could shed light on the QCD phase transition along with critical point in heavy-ion collisions.