  We derive the first systematic observational constraints on reheating in
models of inflation where an additional light scalar field contributes to
primordial density perturbations and affects the expansion history during
reheating. This encompasses the original curvaton model but also covers a
larger class of scenarios. We find that, compared to the single-field case,
lower values of the energy density at the end of inflation and of the reheating
temperature are preferred when an additional scalar field is introduced. For
instance, if inflation is driven by a quartic potential, which is one of the
most favoured models when a light scalar field is added, the upper bound
$T_{\mathrm{reh}}<5\times 10^{4}\,\mathrm{GeV}$ on the reheating temperature
$T_{\mathrm{reh}}$ is derived, and the implications of this value on
post-inflationary physics are discussed. The information gained about reheating
is also quantified and it is found that it remains modest in plateau inflation
(though still larger than in the single-field version of the model) but can
become substantial in quartic inflation. The role played by the vev of the
additional scalar field at the end of inflation is highlighted, and opens
interesting possibilities for exploring stochastic inflation effects that could
determine its distribution.
