We present simulations of coronal mass ejections (CMEs) performed with a new two-temperature coronal model developed at the University of Michigan, which is able to address the coupled thermodynamics of the electron and proton populations in the context of a single fluid. This model employs heat conduction for electrons, constant adiabatic index (γ = 5/3), and includes Alfvén wave pressure to accelerate the solar wind. The Wang-Sheeley-Arge empirical model is used to determine the Alfvén wave pressure necessary to produce the observed bimodal solar wind speed. The Alfvén waves are dissipated as they propagate from the Sun and heat protons on open magnetic field lines to temperatures above 2 MK. The model is driven by empirical boundary conditions that includes GONG magnetogram data to calculate the coronal field, and STEREO/EUVI observations to specify the density and temperature at the coronal boundary by the Differential Emission Measure Tomography method. With this model, we simulate the propagation of fast CMEs and study the thermodynamics of CME-driven shocks. Since the thermal speed of the electrons greatly exceeds the speed of the CME, only protons are directly heated by the shock. Coulomb collisions low in the corona couple the protons and electrons allowing heat exchange between the two species. However, the coupling is so brief that the electrons never achieve more than 10% of the maximum temperature of the protons. We find that heat is able to conduct on open magnetic field lines and rapidly propagates ahead of the CME to form a shock precursor of hot electrons.