  The thermodynamic evolution of Coronal Mass Ejections (CMEs) in the inner
corona (< 1.5 R$_{sun}$) is not yet completely understood. In this work, we
study the evolution of thermodynamic properties of a CME core observed in the
inner corona on July 20, 2017, by combining the MLSO/K-Cor white-light and the
MLSO/CoMP Fe XIII 10747 {\AA} line spectroscopic data. We also estimate the
emission measure weighted temperature (T$_{EM}$) of the CME core by applying
the Differential Emission Measure (DEM) inversion technique on the SDO/AIA six
EUV channels data and compare it with the effective temperature (T$_{eff}$)
obtained using Fe XIII line width measurements. We find that the T$_{eff}$ and
T$_{EM}$ of the CME core show similar variation and remain almost constant as
the CME propagates from ~1.05 to 1.35 R$_{sun}$. The temperature of the CME
core is of the order of million-degree kelvin, indicating that it is not
associated with a prominence. Further, we estimate the electron density of this
CME core using K-Cor polarized brightness (pB) data and found it decreasing by
a factor of ~ 3.6 as the core evolves. An interesting finding is that the
temperature of the CME core remains almost constant despite expected adiabatic
cooling due to the expansion of the CME core, which suggests that the CME core
plasma must be heated as it propagates. We conclude that the expansion of this
CME core behaves more like an isothermal than an adiabatic process.
