  We consider type IIA compactification on $K3$. We show that the instanton
subsectors of the worldvolume of $N$ 4-branes wrapped around $K3$ lead to a
Hagedorn density of BPS states in accord with heterotic-type IIA duality in 6
dimensions. We also find evidence that the correct framework to understand the
results of Nakajima on the appearance of affine Kac-Moody algebras on the
cohomology of moduli space of instantons on ALE spaces is in the context of
heterotic-type IIA string duality.
