  We study anti-self-dual Yang-Mills instantons on $\mathbb{R}^{3}\times
S^{1}$, also known as calorons, and their behaviour under collapse of the
circle factor. In this limit, we make explicit the decomposition of calorons in
terms of constituent pieces which are essentially charge $1$ monopoles. We give
a gluing construction of calorons in terms of the constituents and use it to
compute the dimension of the moduli space. The construction works uniformly for
structure group an arbitrary compact semi-simple Lie group.
