Casimir Effect at finite temperature for the CPT-even extension of QED

By the thermofield dynamics (TFD) formalism we obtain the energy-momentum tensor for the Electromagnetism with Lorentz Breaking Even term of the Standard Model Extended (SME) Sector in a topology $S^{1}\times S^{1}\times R^{2}$. We carry out the compactification by a generalized TFD-Bogoliubov transformation that is used to define a renormalized energy-momentum tensor, and the Casimir energy and pressure at finite temperature are then derived. A comparative analysis with the electromagnetic case is developed, and we remark the influence of the background in the traditional Casimir effect.