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We extend the self-consistent Hartree-Fock-Popov calculations by Nikuni et al. [Phys. Rev. Lett. 84, 5868 (2000)] concerning the Bose-Eistein condensation of magnons in TlCuCl3 to include a realistic dispersion of the excitations. The result for the critical field as a function of temperature behaves as Hc(T)-Hc(0) T^3/2 below 2K but deviates from this simple power-law at higher temperature and is in very good agreement with the experimental results. The specific heat is computed as a functiondoi:10.1143/jpsj.73.3429 fatcat:h5kockxcerdkpeaxlcba5cd2xy