We report on the results of our simulations of an InGaAsInAlAs midinfrared quantum cascade laser (QCL) designed to operate in continuous wave mode at room temperature [Beck, Science 295, 301 (2002)]. Our physical model of the device consists of a self-consistent solution of the subband population rate equations and accounts for all electron-longitudinal-optical phonon and electron-electron scattering rates, as well as an evaluation of the temperature of the nonequilibrium electron distribution. We also consider the role of the doping density and its influence on the electron dynamics. We found that the temperature of the nonequilibrium electron distribution differed significantly from the lattice temperature and that this temperature increased with applied electric field and current density, with coupling constants somewhat larger than analogous GaAs based midinfrared QCLs. Our simulations also reveal physical processes of the device that are not apparent from the experimental measurements, such as the role of electron-electron scattering.