  We derive a one-parameter family of gauged Skyrme models from Yang-Mills
theory on $S^1\times\mathbb{R}^3$, in which skyrmions are well-approximated by
calorons and monopoles. In particular we study the spherically symmetric
solutions to the model with two distinct classes of boundary conditions, and
compare them to calorons and monopoles. Calorons interpolate between instantons
and monopoles in certain limits, and we observe similar behaviour in the
constructed gauged Skyrme model in the weak and strong coupling limits. This
comparison of calorons, monopoles, and skyrmions may be a way to further
understand the apparent relationships between skyrmions and monopoles on
$\mathbb{R}^3$.
