Magnetohydrodynamic (MHD) turbulence plays an important role for the fast energy release and wave structures related to coronal mass ejections (CMEs). The CME plasma has been observed to be strongly heated during solar eruptions, but the heating mechanism is not understood. In this paper, we focus on the hot, dense region at the bottom of the CME and the generation of coronal wave trains therein using a high-resolution 2.5D MHD simulation. Our results show that the interaction between the tearing current sheet and the turbulence, including the termination shocks (TSs) at the bottom of the CME, can make a significant contribution to heating the CME, and the heating rate in this region is found to be greater than the kinetic energy transfer rate. Also, the turbulence can be somewhat amplified by the TSs. The compression ratio of the TS under the CME can exceed 4 due to thermal conduction, but such a strong TS is hardly detectable in all Solar Dynamics Observatory/Atmospheric Imaging Assembly bands. And turbulence is an indispensable source for the periodic generation of coronal wave trains around the CME.