We show that recent treatments of magnetically trapped Bose-Einstein conden
sates (BECs) at temperature T > 0 fit a simple picture: the condensate wave
function is that of a T = 0 BEC with the appropriate (depleted) number of c
ondensate atoms N-0, and the surrounding thermal cloud is described by the
statistical mechanics of an ideal gas in the combined potentials of the mag
netic trap and the cloud-condensate interaction. Even a simple classical de
scription of the cloud reproduces its essential outline, and facilitates ea
sy approximate calculations of BEC properties for T > 0.