Dielectric elastomers (DEs) are increasingly used in applications like lenses, smart skins, and acoustic actuators due to their large electromechanical deformation and viscoelastic properties. This study focuses on the dynamic behavior of a circular-shaped DE membrane, which differs from regular membranes in its energy response to changes in frequency or temperature. The analysis uses energy-based methods like the Euler–Lagrange equation to model the homogeneous deformation under sinusoidal electrical loading, considering the viscoelasticity of DEs. A two-chain network model, with one chain representing elasticity and the other relaxation, is employed, and temperature-dependent permittivity is assumed. By solving the system using Simulink, the relation between stretch ratios and varying temperatures is determined. The results show that higher temperatures lead to lower natural frequencies but increased amplitude, with a quasi-periodic system behavior. Stretch values at resonance are significantly higher than at other frequencies, offering insights for extending the process to other hyperelastic materials.