  Let $G$ be a split semisimple group over a function field. We prove the
temperedness at unramified places of automorphic representations of $G$,
subject to a local assumption at one place, stronger than supercuspidality, and
assuming the existence of cyclic base change with good properties. Our method
relies on the geometry of $\operatorname{Bun}_G$. It is independent of the work
of Lafforgue on the global Langlands correspondence.
