  A generalization of the Bogoliubov transformation is developed to describe a
space compactified fermionic field. The method is the fermionic counterpart of
the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.
C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on
the thermofield dynamics approach. We analyse the energy-momentum tensor for
the Casimir effect of a free massless fermion field in a $d$-dimensional box at
finite temperature. As a particular case the Casimir energy and pressure for
the field confined in a 3-dimensional parallelepiped box are calculated. It is
found that the attractive or repulsive nature of the Casimir pressure on
opposite faces changes depending on the relative magnitude of the edges. We
also determine the temperature at which the Casimir pressure in a cubic boc
changes sign and estimate its value when the edge of the cybe is of the order
of confining lengths for baryons.
