We propose an instanton-based random matrix model of the lowest part
of the spectrum of the Dirac operator in the high temperature phase of
quantum chromodynamics. Our model differs in two important ways from
previously considered similar instanton models. Firstly, it is extremely
simple, having only two parameters, one of which is the topological
susceptibility. Secondly, it provides an excellent description of the
distribution of the lowest eigenvalues of the Dirac operator, obtained from
quenched lattice simulations with the overlap operator. We argue that the
singular spike in the Dirac spectrum at zero is due to a gas of free
instantons, and we show that for two chiral flavors, the $U(1)_A$
symmetry breaking pion minus delta susceptibility remains nonzero in the
chiral limit.