During Carrington rotation (CR) 2107, a fast coronal mass ejection (CME; >2000 km s −1) occurred in active region NOAA 11164. This event is also associated with a solar energetic particle event. In this study, we present simulations of this CME with one-temperature (1T) and two-temperature (2T: coupled thermodynamics of the electron and proton populations) models. Both the 1T and 2T models start from the chromosphere with heat conduction and radiative cooling. The background solar wind is driven by Alfvén-wave pressure and heated by Alfvén-wave dissipation in which we have incorporated the balanced turbulence at the top of the closed field lines. The magnetic field of the inner boundary is set up using a synoptic map from Solar Dynamics Observatory/ Helioseismic and Magnetic Imager. The Titov–Démoulin flux-rope model is used to initiate the CME event. We compare the propagation of fast CMEs and the thermodynamics of CME-driven shocks in both the 1T and 2T CME simulations. Also, the synthesized white light images are compared with the Solar and Heliospheric Observatory/ Large Angle and Spectrometric Coronagraph observations. Because there is no distinction between electron and proton temperatures, heat conduction in the 1T model creates an unphysical temperature precursor in front of the CME-driven shock and makes the shock parameters (e.g., shock Mach number, compression ratio) incorrect. Our results demonstrate the importance of the electron heat conduction in conjunction with proton shock heating in order to produce the physically correct CME structures and CME-driven shocks. Key words: interplanetary medium – magnetohydrodynamics (MHD) – methods: numerical – solar wind – Sun: corona – Sun: coronal mass ejections (CMEs) Online-only material: color figures