  One of the prominent decay modes of heavy nuclei which are produced in
astrophysical environments at temperatures of the order of $10^9$ K is the
$\alpha$ ($^4$He) decay. Thermally enhanced $\alpha$ decay rates are evaluated
within the standard scheme of a tunneling decay where the $\alpha$ particle
tunnels through the potential barrier formed by its interaction with the
daughter nucleus. Following the observation that there exist several excited
levels with the possibility of an $\alpha$ decay when the daughter nucleus is
at a shell closure, we focus in particular on decays producing daughter nuclei
with the neutron number, N = 126. Within a statistical approach we find that
the half-lives, $t_{1/2}(T)$, for temperatures ranging from $T$ = 0 to 2.4 GK
can decrease by 1 - 2 orders of magnitude with the exception of the decay of
$^{212}$Po which decays to the doubly magic daughter $^{208}$Pb, where
$t_{1/2}(T)$ decreases by 5 orders of magnitude. The effect of these thermally
enhanced $\alpha$ decays on the $r$-process nucleosynthesis can be significant
in view of the mass build up at the waiting point nuclei with closed neutron
shells.
