  We address the problem of identifying the critical temperature in a crossover
from the Bose-Einstein condensed (BEC) phase to the normal phase. For this
purpose we study the temperature dependence of magnetization of spin-gapped
quantum magnets described by BEC of triplons. We have calculated the heat
capacity $C_H$ at constant field and fluctuations in magnetization in a
spin-gapped quantum magnet using the Hartree-Fock-Bogouliubov approximation and
found optimized parameters of the Hamiltonian of triplon gas.
  In the region of phase transition, the heat capacity $C_H$ is smeared out due
to the Dzyaloshinsky-Moriya (DM) interaction. The sharp maximum of the
fluctuations in the magnetization is identified as the critical temperature of
the crossover.
