  In this paper we constrain some aspects of the general postinflationary phase
in the context of superconformal $\alpha$-attractor models of inflation. In
particular, we provide constraints on the duration of the reheating process,
$N_{reh}$, and on the reheating temperature, $T_{reh}$, simulating possible and
future results given by the next-generation of cosmological missions. Moreover,
we stress what kinds of equation-of-state parameter, $w_{reh}$, are favored for
different scenarios. The analysis does not depend on the details of the
reheating phase and it is performed assuming different measurements of the
tensor-to-scalar ratio $r$.
