Comparison of the derived (T, β) values in the case of simulated modified black body spectra of different noise level (cf. Sect. 4). The black solid lines correspond to the relation assumed in the simulation of the observations. The measurements have 5% or 10% relative errors or the absolute errors described in Sect. 4.3. In the fourth column of frames, the observations follow two distinct β(T) relations (black solid lines) with 20% relative errors for the low temperature branch (T < 15 K) and 5% relative errors for the high temperature branch (T > 14 K). The left-hand frames show some MCMC samples (coloured dots), their averages (red circles) and the fitted β(T) relations (dashed blue lines). The right hand frames show the distributions for the errors ΔT and Δβ. The plots correspond to a single noise realisation of observations of 50 sources.