  For high-redshift submillimetre or millimetre sources detected with single
dish telescopes, interferometric follow-up has shown that many are multiple
submm galaxies blended together. Confusion-limited Herschel observations of
such targets are also available, and these sample the peak of their spectral
energy distribution in the far-infrared. Many methods for analysing these data
have been adopted, but most follow the traditional approach of extracting
fluxes before model spectral energy distributions are fit, which has the
potential to erase important information on degeneracies among fitting
parameters and glosses over the intricacies of confusion noise. Here, we adapt
the forward-modelling method that we originally developed to disentangle a
high-redshift strongly-lensed galaxy group, in order to tackle this problem in
a more statistically rigorous way, by combining source deblending and SED
fitting into the same procedure. We call this method "SEDeblend." As an
application, we derive constraints on far-infrared luminosities and dust
temperatures for sources within the ALMA follow-up of the LABOCA Extended
Chandra Deep Field South Submillimetre Survey. We find an average dust
temperature for an 870 micron-selected sample of (33.9+-2.4) K for the full
survey. When selection effects of the sample are considered, we find no
evidence that the average dust temperature evolves with redshift.
