  Energy dependence of specific heat extracted from temperature fluctuation of
Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV to 200 GeV was investigated by
using a multiphase transport (AMPT) model. The results were compared with those
from other models and some differences at low $\sqrt{s_{NN}}$ were found. To
explain the above differences and describe the properties of the hot dense
matter at low $\sqrt{s_{NN}}$, a new quantity $C_v^{*}$ was derived for
describing specific heat in heavy-ion collisions. It was found that, by using
$C_v^{*}$ together with its high order moments (skewness and kurtosis), thermal
properties of the hot dense matter can be described and different thermal
properties with or without parton process can be clearly distinguished. The
proposed observable provides a way to learn the property of QCD matter % phase
transition %along with critical point in heavy-ion collisions.
