In the paper at hand, computational analysis of material stability in electro-active polymers (EAP) is considered with taking into account coupling between the thermal, electrical and mechanical fields. To this end, a mixed Hu–Washizu-type thermo-electro-mechanical finite element formulation is proposed. Both, fully monolithic and partitioned finite element formulations are briefly described and employed to simulate the coupled response of homogeneous and inhomogeneous EAP, under varying temperatures. The partitioned finite element approach, which is based on a split of the problem into electro-mechanical and thermal sub-problems, is utilized to carry out material stability analysis on the Gauss point level. The structural response beyond the material-instability point is traced.