The predictive simulation of soft active materials, such as Electro-Active Polymers (EAPs), requires constitutive models that can capture the non-linear coupling between large deformations, electric fields, and thermal fluctuations. This work presents a framework for finite strain thermo-electro-viscoelasticity, addressing the full pipeline from thermodynamic formulation and numerical implementation to experimental calibration. The proposed model introduces two distinct features to ensure rigorous thermodynamic consistency. First, the viscoelastic response is governed by a multiplicative decomposition of the deformation gradient coupled with a stress-driven evolution law, offering a robust description of dissipative mechanisms analogous to return-mapping algorithms [1]. Second, we enforce the fulfilment of the Third Law of Thermodynamics [2] by defining a deformation-dependent specific heat capacity. This correction ensures vanishing entropy at absolute zero and guarantees the poly-convexity. These fields are coupled in an energy-momentum scheme [3]. The numerical implementation is developed in the Julia programming language. The tangent operators are derived analytically and tested via automatic differentiation, ensuring optimal convergence. This computational efficiency is critical for the parameter identification phase. A contribution of this work is the calibration of the material parameters using experimental data for VHB polymer. We formulate the identification process as an inverse optimization problem, minimizing the error between the model predictions and experimental data. The results demonstrate that the proposed model captures complex rate-dependent behaviours and electro-mechanical coupling with high fidelity. Finally, the calibrated model is employed to simulate 3D boundary value problems, showcasing its capability to predict self-heating and actuation in soft robotic scenarios. The group acknowledges the financial support received via project POTENTIAL (PID2022-141957OB-C21 and PID2022-141957OA-C22) funded by MICIN/AEI/10.13039/501100011033/ FEDER, UE.