  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.
