Internal shocks occurring in blazars may accelerate both thermal and non-thermal electrons. While the non-thermal tail fills the higher end of the electron energy distribution (EED), thermal electrons populate the lowest energies of the shock-accelerated particles. In this paper, we examine the consequences that such a hybrid (thermal-non-thermal) EED has on the spectrum of blazars. Since the thermal component of the EED may extend to very low energies, the synchrotron emission of ultrarelativistic electrons may not be sufficiently accurate to compute blazar spectra. Thus, we replace the standard synchrotron process by the more general magneto-bremsstrahlung (MBS) mechanism encompassing the discrete emission of harmonics in the cyclotron regime, the transition from the discrete to continuum and the continuum emission in the synchrotron realm. In the γ-ray band, an EED of mostly thermal particles displays significant differences with respect to the one dominated by non-thermal particles. A thermally dominated EED produces a synchrotron self-Compton (SSC) peak extending only up to a few MeV, and the valley separating the MBS and the SSC peaks is much deeper than if the EED is dominated by non-thermal particles. The combination of these effects modifies the Compton dominance of a blazar, suggesting that the vertical scatter in the distribution of FSRQs and BL Lacs in the peak synchrotron frequency-Compton dominance parameter space could be attributed to different proportions of thermal/non-thermal particles in the EED of blazars.