Because of their viscoelasticity, dielectric elastomers (DEs) are able to produce a large time-dependent electromechanical deformation. In the current study, we use the Euler-Lagrange equation to characterize the influence of temperature, excitation frequency, and viscoelasticity on the dynamic electromechanical deformation and stability of viscoelastic dielectrics. We investigate the time-dependent dynamic performance, hysteresis, phase diagram, and Poincaré map associated with the viscoelastic dissipative process. The results show that the dynamic response has strong temperature and frequency dependencies. It is observed that the natural frequency of the DE decreases with increasing temperature and the maximal amplitude increases at higher temperatures. At relative low frequencies, the amplitude is very small and the viscoelasticity has a significant effect on the oscillation of the system. Furthermore, the results show that the viscoelasticity has a relatively major influence on the dynamic performance for DEs that have very low relaxation times.