  We investigate how uncertainties in flux measurements affect the results from
modified blackbody SED fits. We show that an inverse correlation between the
dust temperature T and spectral index (beta) naturally arises from least
squares fits due to the uncertainties, even for sources with a single T and
beta. Fitting SEDs to noisy fluxes solely in the Rayleigh-Jeans regime produces
unreliable T and beta estimates. Thus, for long wavelength observations (lambda
>~ 200 micron), or for warm sources (T >~ 60 K), it becomes difficult to
distinguish sources with different temperatures. We assess the role of noise in
recent observational results that indicate an inverse and continuously varying
T - beta relation. Though an inverse and continuous T - beta correlation may be
a physical property of dust in the ISM, we find that the observed inverse
correlation may be primarily due to noise.
