  Upon its completion the Herschel ATLAS (H-ATLAS) will be the largest
submillimetre survey to date, detecting close to half-a-million sources. It
will only be possible to measure spectroscopic redshifts for a small fraction
of these sources. However, if the rest-frame spectral energy distribution (SED)
of a typical H-ATLAS source is known, this SED and the observed Herschel fluxes
can be used to estimate the redshifts of the H-ATLAS sources without
spectroscopic redshifts. In this paper, we use a subset of 40 H-ATLAS sources
with previously measured redshifts in the range 0.5<z<4.2 to derive a suitable
average template for high redshift H-ATLAS sources. We find that a template
with two dust components T_c = 23.9 K, T_h = 46.9 K and ratio of mass of cold
dust to mass of warm dust of 30.1) provides a good fit to the rest-frame fluxes
of the sources in our calibration sample. We use a jackknife technique to
estimate the accuracy of the redshifts estimated with this template, finding a
root mean square of Delta z/(1+z) = 0.26. For sources for which there is prior
information that they lie at z > 1 we estimate that the rms of Delta z/(1+z) =
0.12. We have used this template to estimate the redshift distribution for the
sources detected in the H-ATLAS equatorial fields, finding a bimodal
distribution with a mean redshift of 1.2, 1.9 and 2.5 for 250, 350 and 500 um
selected sources respectively. \end{abstract}
