  The investigation of the fluctuations in interacting quantum systems at
finite temperatures showcases the ongoing challenges in understanding complex
quantum systems. Recently, atom number fluctuations in weakly interacting
Bose-Einstein condensates were observed, motivating an investigation of the
thermal component of partially condensed Bose gases. Here, we present a
combined analysis of both components, revealing the presence of fluctuations in
the thermal component. This analysis includes a comprehensive statistical
evaluation of uncertainties in the preparation and parameter estimation of
partially condensed Bose gases. Using Monte Carlo simulations of optical
density profiles, we estimate the noise contributions to the atom number and
temperature estimation of the condensed and thermal cloud, which is generally
applicable in the field of ultracold atoms. Furthermore, we investigate the
specific noise contributions in the analysis of atom number fluctuations and
show that preparation noise in the total atom number leads to an important
technical noise contribution. Subtracting all known noise contributions from
the variance of the atom number in the BEC and thermal component allows us to
improve the estimate of the fundamental peak fluctuations.
