  The shift in condensation temperature caused by interactions is studied up to
second order in the s-wave scattering length in a Bose-Einstein condensate
trapped in a temperature-dependent three-dimensional generic potential. With no
assumptions other than the mean-field approach and semiclassical approximations
it is shown that the inclusion of a temperature-dependent trap improves the
empirical values of the numerical parameters compared to those obtained in
previous reports on the temperature shift.
