We consider Chern–Simons theory on a 3-manifold M that is the total space of a circle bundle over a 2d base Σ . We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with structure group given by the full affine level k central extension of the loop group L G . The space of fields of this 2d theory is naturally symplectic, and this provides a new formulation of a result of Beasley–Witten about the equivariant localization of the Chern–Simons path integral. The main tool that we employ is the Caloron correspondence, originally due to Murray–Garland, that relates the space of gauge fields on M with a certain enlarged space of connections on an equivariant version of the loop space of the G -bundle. We show that the symplectic structure that Beasley–Witten found is related to a looped version of the Atiyah–Bott construction in 2-dimensional Yang–Mills theory. We also show that Wilson loops that wrap a single circle fiber are also described very naturally in this framework.