  The problem of a scalar particle in a constant crossed electromagnetic field
($\mathbf{E}\perp\mathbf{H}$ and $|\mathbf{E}|=|\mathbf{H}|$) is examined. The
high-temperature expansion of the grand thermodynamic potential and vacuum
energy with account for non-perturbative corrections are derived. The
contribution from particles and antiparticles is considered separately. It is
shown that the non-perturbative corrections depend on boundary conditions but
do not depend on fields.
