  We combine submm photometric data of z>4 quasars, to obtain a mean
far-infrared (FIR) (rest-frame) spectral energy distribution (SED) of thermal
emission from dust, parameterised by a single temperature (T) and power-law
emissivity index (beta). Best-fit values are T=41+/-5K, beta=1.95+/-0.3. The
redshift spread of this set of quasars is exploited to allow us to sample the
SED at a greater number of rest wavelengths than is possible for a single
object. This parameterisation is of use to any study that extrapolates from a
flux at a single submm wavelength, for example to infer dust masses and FIR
luminosities. We then interpret the submm component as arising from dust heated
by star-formation in the quasar's host galaxy, and investigate a simple scheme
of AGN--host coevolution, in which the timescale for formation of the host
galaxy is c.0.5-1.0Gyr, with star formation proceeding at a constant rate
c.1000Msol/yr. The luminous quasar phase occurs towards the end of the
star-forming period, just before the galaxy's reservoir of cold gas is
depleted. Given the youth of the Universe at z=4 (1.6Gyr), the coexistence of a
massive black hole and a luminous starburst can be a powerful constraint on
models of quasar host-galaxy formation.
