  The formulation for zero mode of a Bose-Einstein condensate beyond the
Bogoliubov approximation at zero temperature [Y.Nakamura et al., Phys. Rev. A
89, 013613 (2014)] is extended to finite temperature. Both thermal and quantum
fluctuations are considered in a manner consistent with a concept of
spontaneous symmetry breakdown for a finite-size system. Therefore, we need a
proper treatment of the zero mode operators, which invoke non-trivial
enhancements in depletion condensate and thermodynamical quantities such as the
specific heat. The enhancements are visible in the weak interaction case. Our
approach reproduces the results of a homogeneous system in the Bogoliubov
approximation in a large particle number limit.
