  We present a radiative-transfer calculation which reproduces the infrared
spectrum of the planetary nebula BD~+30$^{\circ}$3639. We calculate the
transfer process through absorption and scattering in a spherical-symmetric
multi-grain dust shell. The emission of transiently heated particles is taken
into account, as well as polycyclic aromatic hydrocarbons. We obtain an
acceptable fit to most of the spectrum, including the PAH infrared bands. At
submillimetre wavelengths the observed emission is larger than the model
predicts, indicating that large dust conglomerates (``f{}luffy grains'') may be
needed as an additional constituent. The fit favours a distance of $\ge 2
\,$kpc, which implies that BD~+30$^\circ$3639 has evolved from a massive
progenitor of several solar masses. A low dust-to-gas mass ratio is found in
the ionised region. The calculations yield an original mass-loss rate of
$2\times10^{-4} \msolar \peryr$ on the Asymptotic Giant Branch. Using this
mass-loss rate, we calculate how the infrared spectrum has evolved during the
post-AGB evolution. We show in particular the evolution of the IRAS colours
during the preceding post-AGB evolution.
