In non-isothermal dielectric fluids subject to electric fields, the coupling between electric and temperature fields through the thermal variation of permittivity gives rise to an electrohydrodynamic force and can generate convective motion in fluids [see, e.g., Yoshikawa et al., 87, 043003, 2013]. The convection driven by this thermo-electrohydrodynamic effect is of importance in active control of heat and mass transport in small fluid systems, e.g., for manipulation of particles to modify locally their concentration [Kumar et al. Langmuir, 26(7), 5262-5272, 2010]. By the linear stability theory, we investigate instabilities provoked by the TEHD force in Taylor-Couette (TC) flow systems subject to radial temperature gradient and electric field. Different TC systems of different gap widths in different gravitational environments, i.e., in microgravity and on the Earth are considered. Depending on the radius ration of inner to outer cylinders and on the gravitational condition, different instabilities are observed. We elucidate the driving effects of different instabilities by an energetic analysis. We also examine effects of dielectric loss on the instabilities.