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We extend earlier models of the growth of a Bose-Einstein condensate toinclude the full dynamical effects of the thermal cloud by numerically solvinga modified quantum Boltzmann equation. We determine the regime in which theassumptions of the simple model are a reasonable approximation, and compare ournew results with those that were earlier compared with experimental data. Wefind good agreement with our earlier modelling, except at higher condensatefractions, for which a significant speedup is found. We also investigate theeffect of temperature on condensate growth, and find that this has asurprisingly small effect.  The discrepancy between theory and experiment remains, since the speedupfound in these computations does not occur in the parameter regime specified inthe the experiment.Comment: Fourteen pages, TeX source with 11 figures. Changes : Extended  section on formalism to include a derivation of the ergodic Boltzmann  equation that we use, and a fuller explanation of the numerical methods.  Explained more fully the possible errors with the experimental data. Added  section detailing the source of possible errors in this formulation. Added  comparison of our work with the manuscript cond-mat/0001323, and some  analysis of the fits to the MIT growth curve

Quantum kinetic theory. VII. The influence of vapor dynamics on condensate growth