  In this work I investigate the finite temperature Casimir effect due to a
massive and charged scalar field that breaks Lorentz invariance in a CPT-even,
aether-like way. I study the cases of Dirichlet and mixed (Dirichlet-Neumann)
boundary conditions on a pair of parallel plates. I will not examine the case
of Neumann boundary conditions since it produces the same results as Dirichlet
boundary conditions. The main tool used in this investigation is the
$\zeta$-function technique that allows me to obtain the Helmoltz free energy
and Casimir pressure in the presence of a uniform magnetic field perpendicular
to the plates. Three cases of Lorentz asymmetry are studied: timelike,
spacelike and perpendicular to the magnetic field, spacelike and parallel to
the magnetic field. Asymptotic cases of small plate distance, high temperature,
strong magnetic field, and large mass will be considered for each of the three
types of Lorentz asymmetry and each of the two types of boundary conditions
examined. In all these cases simple and very accurate analytic expressions of
the thermal corrections to the Casimir energy and pressure are obtained and I
discover that these corrections strongly depend on the direction of the unit
vector that produces the breaking of the Lorentz symmetry.
