We show that recent treatments of magnetically trapped Bose-Einstein condensates (BECs) at temperature T>0 fit a simple picture: the condensate wavefunction is that of a T = 0 BEC with the appropriate (depleted) number of condensate atoms N₀, and the surrounding thermal cloud is described by the statistical mechanics of an ideal gas in the combined potentials of the magnetic trap and the cloud-condensate interaction. Even a simple classical description of the cloud reproduces its essential outline, and facilitates easy approximate calculations of BEC properties for T>0.