  We prove a gluing theorem on the automorphic side of the geometric Langlands
correspondence: roughly speaking, we show that the difference between
$\mathrm{DMod}(\mathrm{Bun}_G)$ and its full subcategory
$\mathrm{DMod}(\mathrm{Bun}_G)^\mathrm{temp}$ of tempered objects is
compensated by the categories $\mathrm{DMod}(\mathrm{Bun}_M)^\mathrm{temp}$ for
all standard Levi subgroups $M \subsetneq G$. This theorem is designed to match
exactly with the spectral gluing theorem, an analogous result occurring on the
other side of the geometric Langlands conjecture. Along the way, we state and
prove several facts that might be of independent interest. For instance, for
any parabolic $P \subseteq G$, we show that the functors
$\mathrm{CT}_{P,*}:\mathrm{DMod}(\mathrm{Bun}_G) \to
\mathrm{DMod}(\mathrm{Bun}_M)$ and $\mathrm{Eis}_{P,*}:
\mathrm{DMod}(\mathrm{Bun}_M) \to \mathrm{DMod}(\mathrm{Bun}_G)$ preserve
tempered objects, whereas the standard Eisenstein functor $\mathrm{Eis}_{P,!}$
preserves anti-tempered objects.
