  We investigate the effect of non-zero temperature to the condensate fraction
of a homogeneous dilute weakly interacting Bose gas in very low-temperature
region. Within inproved Hartree-Fock approximation, the
Cornwall-Jackiw-Tomboulis effective action approach shows that the thermal
fluctuations make the condensate fraction decrease as a second and fourth-order
power law of temperature. The result is compared with experimental data.
Indeed, the effect of non-infinite size of the trap is also integrated.
