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A simple picture describes the results of recent treatments ofpartially-condensed, dilute, trapped Bose gases at temperature T > 0. Thecondensate wavefunction is nearly identical to that of a T=0 condensate withthe same number of condensate atoms, N_0. The cloud of non-condensed atoms isdescribed by the statistical mechanics of an ideal Bose gas in the combinedpotentials of the magnetic trap and the cloud-condensate interaction. Weprovide a physical motivation for this result, show how it emerges in theHartree-Fock-Bogoliubov-Popov approximation, and explore some of itsimplications for future experiments.

Trapped Bose-einstein Condensates at Finite Temperature: a Two-gas Model