  We have investigated experimentally the finite-temperature properties of a
Bose-Einstein condensed cloud of $^{87}$Rb atoms in a harmonic trap. Focusing
primarily on condensed fraction and expansion energy, we measure unambiguous
deviations from ideal-gas thermodynamics, and obtain good agreement with a
Hartree-Fock description of the mixed cloud. Our results offer for the first
time clear evidence of the mutual interaction between the condensed and thermal
components. To probe the low-temperature region unaccessible to the usual
time-of-flight technique, we use coherent Bragg scattering as a filtering
technique for the condensate. This allows us to separate spatially the
condensed and normal components in time of flight, and to measure reliably
temperatures as low as $0.2 T_{\rm c}^0$ and thermal fractions as low as
10%.Finally, we observe evidence for the limitations of the usual image
analysis procedure, pointing out to the need for a more elaborate model of the
expansion of the mixed cloud.
